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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 301. |
An experiment takes `10` minutes to raise the temperature of water in a container from `0^(@)C "to" 100^(@)C` and another `55` minutes to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of water to be `1 "cal//g ^(@)C`, the heat of vapourization according to this experiment will come out to be:-A. `540"cal"//g`B. `530"cal"//g`C. `560"cal"//g`D. `550"cal"//g` |
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Answer» Correct Answer - D Let M is mass of water and P is amount of heat supplied per unit minute. `MS_(W)(100-0) = P xx 10 …..(i)` `ML_(V) = P xx 55 …. (ii)` (i)/(ii) we get `L_(V) = 550"cal"//"g"` |
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| 302. |
The left end of a long glass rod of index 1.6350 is grounded and polished to a convex spherical surface of radius 2.50 cm. A small object is located in the air and on the axis 9.0 cm from the vertex. Find the lateral magnification. |
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Answer» Correct Answer - `-0.0777` |
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| 303. |
A piece of metal is cut from a hollow metal sphere of radius R and is polished on both sides. A boy looks at the metal piece and finds his image 13 cm behind the metal piece. His friend flips the mirror, keeping its position unchanged and now the boy finds his image to be 52 cm behind the mirror. Find R. |
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Answer» Correct Answer - 69.33 cm |
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| 304. |
A small insect starts walking away from a concave mirror along its principal axis. At a point (P) 20 cm from the mirror the image flips upside down. (a) What can you say about the size of the image at the instant it flips upside down – it is very large, very small or of the size similar to the insect? (b) Find the distance of the insect from point (P) where its image is thrice as large as the insect. |
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Answer» Correct Answer - (a) very large (b) 6.67 cm on both sides of P. |
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| 305. |
The focal length of the objective and the eye piece of a compound microscope are 2.0 cm and 3.0 cm, respectively. The distance between the objective and the eye piece is 15.0 cm. The final image formed by the eye piece is at infinity. The two lenses are thin. The distance in cm of the object and the image produced by the objective, measured from the objective lens, are respectivelyA. `2.4` and `12.0`B. `2.4` and `15.0`C. `2.3 `and `12.0`D. `2.3` and `3.0` |
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Answer» Correct Answer - A When final image if formed at infinity, then Length of the tube `=v_(o)+f_(a)=v_(o)=f_(e)` `implies 15=v_(o)+3impliesv_(o)=12 cm` For objective lens `(1)/(f)=(1)/(v_(o))-(1)/(u_(o))` `implies(1)/((+2))=(1)/((+12))-(1)/(u_(o))impliesu_(o)=-2.4cm` |
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| 306. |
An astronomical telescope has an angular magnification of magnitude 5 for distant object. The separation between the objective and the eyepiece is 36 cm and the final image is formed at infinity. The focal length `f_(0)` of the objective and the focal length `f_(0)` of the eyepiece areA. `f_(o)=45cm` and `f_(e)=-9cm`B. `f_(o)=7.2cm` and `f_(e)=5cm`C. `f_(o)=50cm` and `f_(e)=10cm`D. `f_(o)=30cm` and `f_(e)=6cm` |
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Answer» Correct Answer - D In this case `|m|=(f_(o))/(f_(e))=5` …(i) and length of telescope `=f_(o)+f_(e)=36` …(ii) Solving `(i)` and `(ii)` , we get `f_(e)=6cm, f_(o)=60cm` |
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| 307. |
The focal length of objective and eye lens of a astronomical telescope are respectively `2m` and `5 cm` . Final image is formed at `(i)` least distance of distinct vision `(ii)` infinity. The magnifying power in both cases will beA. `-48,-40`B. `-40, -48`C. `-40, 48`D. `-48, 40` |
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Answer» Correct Answer - A When the final image is at the least distance of distinct vision, then `m=(f_(o))/(f_(e))(1+(f_(e))/(D))=(200)/(5)(1+(5)/(25))=(200xx6)/(5xx5)=-48` When the final image at inifinity , then `m=(-f_(o))/(f_(e))=(200)/(5)=-40` |
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| 308. |
Assertion ` :` By increasing the diameter of the objective of telescope, we can increase its range. Reason `:` The range of a telescope tells us how far away a star of some standard brightness can be spotted by telescope.A. If both assertion and reason are true and reason is the correct explanation of assertion.B. If both assertion and reason are true but reason is not the correct explanation of assertion.C. If assertion is true but reason is false.D. If assertion and reason both are false. |
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Answer» Correct Answer - B The light gathering power (or brightness) of a telescope `prop(` diameter `)^(2)`. So by increasing the objective diameter even far off stars may produce images of optimum brightness. |
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| 309. |
A beam of light composed of red and green ray is incident obliquely at a point on the face of rectangular glass slab. When coming out on the opposite parallel face, the red and green ray emerge formA. two points propagating in two different non- parallel directionsB. two points propagating in two different parallel directionsC. one point propagating in two different directionsD. one point propagating in the same directions |
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Answer» Correct Answer - B In any medium other than air or vacuum, the velocities of different colours are different. Therefore, both red and green colours are refracted at different angles of refraction. Hence, after emerging from glass slab through opposite parallel face, they appear at two different points and move in the two different parallel directions. Aliter`:` Angle of refraction will be different, due to which red and green emerge from different points and will be parallel. |
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| 310. |
Statement -`1` : In following figure curve (i) and (iv) represent isothermal process while (ii) & (iii) represent adiabatic process. Statement - `2` :The adiabatic at any point has a steeper slope than the isothermal through the same point .A. Statement -`1` is True , Statement -`2` is True , Statement -`2` is correct explanation for Statement - `1`B. Statement -`1` is True , Statement -`2` is True , Statement -`2` is not correct explanation for Statement - `1`C. Statement -`1` is True , Statement -`2` is False.D. Statement -`1` is False , Statement -`2` is True. |
| Answer» Correct Answer - A | |
| 311. |
Two moles of an ideal monoatomic gas is taken through a cycle ABCA as shown in the P-T diagram. During the process AB , pressure and temperature of the gas very such that `PT=Constant`. It `T_1=300K`, calculate (a) the work done on the gas in the process AB and (b) the heat absorbed or released by the gas in each of the processes. Give answer in terms of the gas constant R. |
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Answer» Correct Answer - (i) ` 1200R` (ii) `Q_(AB) = -2100R, Q_(BC) = 1500R, Q_(CA) = 1200Rln2` (i) Number of moles `n=2 , T_(1) = 300K` During the process `A rarr B` `PT` = constant or `P^(2)V` = constant = K(say) `thereforeP = (sqrtK)/(sqrtV)` `therefore W_(A rarr B) = underset(V_(A))overset(V_(B))intP.dV = underset(V_(A))overset(V_(B))intsqrt(K)/(sqrtV)dV =`2sqrtK[sqrtV_(B)-sqrtV_(A)]=2[sqrtKV_(B) - sqrtKV_(A)]` =`2[sqrt((P_(B)^(2)V_(B))V_(B))-sqrt((P_(A)^(2)V_(A))V_(A))] (K = P^(2)V)` =`2(P_(B)V_(B) -P_(A)V_(A)] = 2[nRT_(B) -nRT_(A)]` =`2nR [T_(1) - 2T_(1)] = (2)(2)(R)[300-600]` =`-1200R`. `therefore` Work done on the gas in the process `AB "is" 1200R`. (ii) Heat absorbed //released in different processes. Since, the gas is monoatomic. Therefore , `C_(V) =(3)/(2)R "and" C_(P)= (5)/(2)R "and" gamma=(5)/(3)` Process A-B : ` DeltaU = nC_(V)DeltaT = (2)((3)/(2)R) (T_(B) - T_(A)) = (2)((3)/(2)R)` `(300-600) = -900R` `therefore Q_(A rarrB) = W_(A rarrB) +DeltaU = (-1200R) - (900R)` `Q_(A rarrB) =-2100R` (Released) Process B-C: Process is isobaric `therefore Q_(B rarrC) = nC_(P)DeltaT` =`(2)((5)/(2)R)(2T_(1) - T_(1))` =`(5R) (600-300)` `Q_(B rarrC) = 1500R` (absorbed) Process C-A : Process is isothermal `DeltaU = 0 "and" Q_(C rarrA) = W_(CrarrA) = nRT_(C)ln((P_(C))/(P_(A)))` =`nR(2T_(1))ln((2P_(1))/(P_(1))) = (2)(R)(600)ln(2)` `Q_(C rarrA) = 831.6R` (absorbed) |
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| 312. |
A plano convex lens `(mu=1.5)` has a maximum thickness of`1mm` .If diameter of its aperture `4cm` Find (i)Radius of curvature of curved surface (ii) its focal length in air. |
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Answer» Correct Answer - (a) 20 cm; (b) 40 cm |
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| 313. |
Which of the following is incorrect regarding the first law of thermodynamics?A. It is applicable to any cyclic processB. It is a restatement of the principle of conservation of energyC. It introduces the concept of the internal energyD. It introduced the concept of the entropy |
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Answer» Correct Answer - D The first law of the thermodynamics does not introduce the concept of entropy |
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| 314. |
A small object of height `0.5` cm is placed in front of a convex surface of glass `(mu-1.5)` of radius of curvature 10cm. Find the height of the image formed in glass. |
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Answer» According to cartesian sign convention, `u=-30cm, R=+10cm, mu_(1)=1,mu_(2)=1.5` Applying the equation, we get ` (1.5)/(v)=(1)/(-30)=(1.5-1)/(+10)` or `v=90cm` (real image) Let `h_(1)` be the height of the image, then `(h_(i))/(h)=(mu_(1)v)/(mu_(2)u)=((1)(90))/((1.5)(-30))=-2` `rArrh_(i)=-2h_(0)(0.5)=-2(0.5)=-1cm` The negative sign shows that the image is inverted. |
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| 315. |
A sphere of radius R made of material of refractive index `mu_(2)` is placed in a medium of refractive index `mu_(1)`. Where would an object be placed so that a real image is formed at equidistant fromk the sphere? ltbgt |
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Answer» Let the object be placed at a distance x from the pole ` P_(1)` of the sphere. If a real image is to be formed at equidistant form the sphere, then the rays must pass symmetrical through the sphere, as shown in the figure is question. Applying the equation at the first surface, we get `(mu_(2))/(+oo)-(mu_(1))/(-x)=(mu_(2)-mu_(1))/(+R)` or `x=((mu_(1))/(mu_(2)-mu_(1)))R` |
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| 316. |
A spherical surface of radius R ssparates two media of refractive indices `mu_(1)` and `mu_(1)` as shown in figure., Where should an object be placed in medium 1 so that a real image is formed in medium 2 at the same distance? |
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Answer» Let x be the distance of the object from the pole in medium 1. Here we have , `u=-x, v=+x and R=+R` Using the equation, we get `(mu_(2))/(+x)-(mu_(1))/(-x) =(mu_(2)-mu_(1))/(+R)` or `x=((mu_(2)+mu_(1))/(mu_(2)-mu_(1)))R` Note that the real image is formed only when `mu_(2) gt mu_(1)` . |
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| 317. |
A lens is 5cm thick and the radii of curvature of its object is placed at a distance of 12cm from the surface whose radius of curvature is 10cm. How far beyond the other surface is the image formed? |
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Answer» We know that `(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R)` `u=-12cm, R=10cm, mu_(1)=1, mu_(2)=1.5` `rArr (1.5)/(v)-(1)/(-12)=(1.5-1)/(10)rArr v=-45 cm` This iamge will serve as an object for the second surface. For the second surface, object distance, `u=5+45=50cm` For the second surface again, `u=-50 cm, R=-25, mu=1.5, mu_(2)=1` `(mu_(2))/(v)-(mu_(1))/(u)=(mu_(2)-mu_(1))/(R)=(1)/(v)-(1.5)/(-50)=(1-1.5)/(-25)` or `v=-100 cm` Find image will be at a distance of `-95 cm` from the first surface on the same side as the object. |
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| 318. |
For an ideal gas `PT^(11)` = constant then volume expansion coefficient is equal to :-A. `(11)/(T)`B. `(1)/(T)`C. `(12)/(T)`D. `(2)/(T)` |
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Answer» Correct Answer - C `PT^(11)` = constant & `PV = nRT` ` implies V alpha T^(12) implies (DeltaV)/(V) = 12(DeltaT)/(T) implies gamma_(v) = (DeltaV)/(VDeltaT) = (12)/(T)` |
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| 319. |
Some of the thermodynamic parameters are state variables while some are process variables. Some grouping of the parameters are given. Choose the correct one.A. State variables: `" "` Temperature , No of moles Process variables : `" "` Internal energy, work done by the gas .B. State variables: `" "` Volume Temperature Process variables : `" "` Internal energy, work done by the gas .C. State variables: `" "` Work done by the gas , heat rejected by the gas Process variables : `" "` Temperature , volume.D. State variables: `" "` Internal energy , volume Process variables : `" "` work done by the gas , heat absorbed by the gas. |
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Answer» Correct Answer - D Internal energy and volume depend upon states. |
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| 320. |
If water at `0^@C` kept in a container with an open top, is placed a large evacuated chamber,A. All the water will vaporize.B. All the water will freeze.C. Part of the water will vaporize and the rest wil freeze.D. Ice, water and water vapour will be formed and reach equilibrium at the triple point. |
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Answer» Correct Answer - C A part of liquid will evaporate immediately sucking latent heat from the bulk of liquid. Hence a part of liquid will freeze. |
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| 321. |
In the previous question, if the specific latent heat of vaporization of water at `0^@C` is `eta` times the specific latent heat of freezing of water at `0^@C`, the fraction of water that will ultimately freeze isA. `(1)/(eta)`B. `(eta)/(eta+1)`C. `(eta-1)/(eta)`D. `(eta-1)/(eta+1)` |
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Answer» Correct Answer - B `DeltaQ_("top") = DeltaQ_("freezing")` `m.(etaL) = M(L) implies M = etam` L = latent heat of freezing m = mass of vapour `M` = mass of freezed `therefore ` Fraction of water which freezed = `(M)/(m+M) = (etaM)/(m + etam) = (n)/(n+1)` |
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| 322. |
A small object is at the bottom of a container which has water filled up to a height of 20 cm. There is a plane mirror inclined at `45°` to the horizontal above the container. A convex lens having focal length 15 cm is at a distance of 50 cm from the mirror. The horizontal principal axis of the lens is at a distance of 45 cm from the bottom of the container. Find the distance of the image (from the lens) of the object as seen by an observer to the left of the lens. Light rays from the object hit the lens only after they are reflected from the mirror. (use `mu_("water") = 4//3)` |
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Answer» Correct Answer - 18 cm |
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| 323. |
Sunrays pass through a pinhole in the roof of a hut and produce an elliptical spot on the floor. The minor and major axes of the spot are 6 cm and 12 cm respectively. The angle subtended by the diameter of the sun at our eye is `0.5°`. Calculate the height of the roof. |
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Answer» Correct Answer - `3.44 cm` |
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| 324. |
The principal axis of a thin equi-convex lens is the x-axis. The co-ordinate of a point object and its image are `(– 20 cm, 1 mm)` and `(25 cm, 2 mm)` respectively. Find the focal length of the lens. |
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Answer» Correct Answer - 90 cm |
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| 325. |
Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is ` 60degree`). In the position of minimum deviation, the angle of refraction will beA. `30^(@)` for both the coloursB. greater for the violet colourC. greater for the red colourD. equal but not `30^(@)` for both the colours |
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Answer» Correct Answer - A In the position of minimum deviation angle of refraction r = `(A)/(2)` |
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| 326. |
Entropy (`S`) is a thermodynamic variable like pressure `P`, volume `V` and temperature `T`. Entropy of a thermodynamic system is a measure of disorder of molecular motion. Greater is disorder , greater is entropy. Change in entropy of a thermodynamic system is the ratio of heat supplied to absolute temperature.In an adiabatic reversible process, entropy remains constant while in any irreversible process entropy increases. In nature the processes are irreversible , therefore entropy of universe is continuoulsy increasing. When milk is heated , its entropy :A. increaseB. decreaseC. remains unchangedD. may decrease or increase |
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Answer» Correct Answer - A When milk is heated, its entropy increases as it is irreversible process. |
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| 327. |
Entropy (`S`) is a thermodynamic variable like pressure `P`, volume `V` and temperature `T`. Entropy of a thermodynamic system is a measure of disorder of molecular motion. Greater is disorder , greater is entropy. Change in entropy of a thermodynamic system is the ratio of heat supplied to absolute temperature.In an adiabatic reversible process, entropy remains constant while in any irreversible process entropy increases. In nature the processes are irreversible , therefore entropy of universe is continuoulsy increasing. The unit of entropy in `S-I` system is -A. `"cal"//K`B. `"joule"//"kg"`C. `"joule"//"k"`D. `"kilocal"//^(@)C` |
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Answer» Correct Answer - C Change in entropy `DeltaS = (DeltaQ)/(T)` `implies ` Unit of entropy = `JK^(-1)` |
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| 328. |
A ray in incident normally on a right angle prism whose refractive index is `sqrt(3)` and prism angle `alpha=30^(@)`. After crossing the prism, ray passes through a glass sphere. It strikes the glass sphere at `(R)/(sqrt(3))` distance from principal axis, as shown in the figure. The is half polished. Find the totol angle of deviation of the incident ray after all reflections and refractions from this optical setup |
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Answer» Correct Answer - `180^(@)` |
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| 329. |
If two mirrors are keps at `60^circ` to each other, then the number of images formed by them isA. 5B. 6C. 7D. 8 |
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Answer» Correct Answer - A The formula for the number of images formed by two inclined mirrors, inclined at angle `theta` is `N = (360)/(theta) -1` If `(360)/(theta)` = even whereas `N = (360)/(theta) "If" (360)/(theta)` = odd For `theta = 60^(@) , N = (360)/(60) = 6 ` Hence , N = 6-1 = 5 |
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| 330. |
A fish is a little away below the surface of a lake. If the critical angle is `49^(@)` , then the fish could see things above the water surface withing an angular range of `theta^(@)` where A. `theta=49^(@)`B. `theta=90^(@)`C. `theta = 90^(@)`D. `theta = 24(1^(@))/(2)` |
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Answer» Correct Answer - C From figure given in question `theta=2c=98^(@)`. |
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| 331. |
A ray of light passes through a rectangular glass block placed in air. Which diagram shows a possible path of a ray? |
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Answer» Correct Answer - Fig (b0 |
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| 332. |
An object is placed at a distance of `f//2` from a convex lens. The image will beA. At one of the foci, virtual and double its sizeB. At `3f//2` , real and invertedC. At `2f, ` virtual and erectD. None of these |
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Answer» Correct Answer - A `(1)/(f)=(1)/(v)+(1)/(u)``(` Given `u=(-f)/(2))` `implies(1)/(f)=( 1)/(v)+((1)/(f//2))implies(1)/(v)=(1)/(f)-(1)/(f)` `implies (1)/(v)=(-1)/(f)` and `m=(v)/(u)=(f)/(f//2)=2` So virtual at the focus and of double size. |
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| 333. |
The ray diagram could be correct A. If `n_(1)=n_(2)=n_(3)`B. If `n_(1)=n_(2)` and `n_(1) lt n_(g)`C. If `n_(1)=n_(2)` and `n_(1) gt n_(g)`D. Under no circumstances |
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Answer» Correct Answer - C If `n_(1)gtn_(g)` then the lens will be in more dense medium. Hence its nature will change and the convex lens will behave like a concave lens. |
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| 334. |
The relation between `n_(1)` and `n_(2)` , if behaviour of light rays is as shown in figure is A. `n_(1)gt gt n_(2)`B. `n_(2)gtn_(1)`C. `n_(1)gtn_(2)`D. `n_(1)=n_(2)` |
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Answer» Correct Answer - B Nature of lens changes, if `mu_(medium )gtmu_(l ens)` |
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| 335. |
Water is used in car radiators as coolant becauseA. of its low boiling pointB. of its high specific heatC. of its low densityD. of its easy availability |
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Answer» Correct Answer - B Water has high specific heat and due to this it absorber more heat In rise of temperature. |
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| 336. |
Two identical masses of `5` kg each fall on a wheel from a height of `10` m . The wheel disturbs a mass of `2` kg water, the rise in temperature of water will be :-A. `2.6^(@)C`B. `1.2^(@)C`C. `0.32^(@)C`D. `0.12^(@)C` |
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Answer» Correct Answer - D Entire `KE` gets converted into heat. `DeltaKE = ms Deltatheta implies 10xx10xx10 = 2xx4200 xxDeltatheta` `implies Deltatheta = 0.12^(@)C` |
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| 337. |
One half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations.A. disappearB. remain almost unaffectedC. have its size reduced to halfD. have its intensity reduced to half. |
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Answer» Correct Answer - D only half of the total rays will form the image so intensity is reduced so half. |
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| 338. |
Assertion `:` Just before setting, the sun may appear to be elliptical. This happens due to refraction. Reason `:` Refraction of light ray through the atmosphere may cause different magnification in mutually perpendicular directions.A. If both assertion and reason are true and reason is the correct explanation of assertion.B. If both assertion and reason are true but reason is not the correct explanation of assertion.C. If assertion is true but reason is false.D. If assertion and reason both are false. |
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Answer» Correct Answer - A When the sun is close to setting, refraction will effect the top part of the sun differently from the bottom half. The top half will radiate its image truly, while the bottom portion will send an apparent image. Since the bottom portion of sun is being seen through thicker, more dense atmosphere, the bottom image is being bent intensely and gives the impression of being squashed or 'flattened' or elliptical shape. |
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| 339. |
Two lenses are placed in contact with each other and the focal length of combination is `80 cm`. If the focal length of one is `20 cm`, then the power of the other will beA. `1.66D`B. `4.00D`C. `-1.00 D`D. `-3.75D` |
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Answer» Correct Answer - D `(1)/(F)=(1)/(f_(1))+(1)/(f_(2))implies(1)/(80)=(1)/(20)+(1)/(f_(2))impliesf_(2)=-(80)/(3)cm` `:.` Power of second lens `P_(2)=(100)/(f_(2))=(100)/(-80//3)=-3.75D` |
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| 340. |
A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of the combination isA. `+1.5`B. `-1.5`C. `+6.67`D. `-6.67` |
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Answer» Correct Answer - B Power of convex lens `P_(1)=(100)/(40)=2.5D` Power of concave lens `P_(2)=-(100)/(25)=-4D` Now `P=P_(1)+P_(2)=2.5D-4D=-1.5D` |
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| 341. |
A convex lens of focal length 40 cm is in contact with a concave lens of focal length 25 cm. The power of the combination isA. `-1.5 D`B. `- 6.5 D`C. `+6.5D`D. `+6.67D` |
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Answer» Correct Answer - A Focal length of the combination can be calculates as `(1)/(F)=(1)/(f_(1))+(1)/(f_(2))implies(1)/(F)implies(1)/((+40))=(1)/((-25))+impliesF=-(200)/(3)cm` `:.` Power of second lens `P=(100)/(F)=(100)/(-200//3)=-1.5 D` |
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| 342. |
A convex lens if in contact with concave lens. The magnitude of the ratio of their focal length is `(2)/(3)`. Their equivalent focal length is 30 cm. What are their individual focal lengths?A. `-75,50`B. `-10,15`C. `75,50`D. `-15,10` |
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Answer» Correct Answer - D `(f_(1))/(f_(2))=(2)/(3)` ....(i) `(1)/(f_(1))-(1)/(f_(2))=(1)/(30)` ....(ii) Solving equations `(i)` and `(ii)` `f_(2)=-15cm` `(` Concave`) ` `f_(1)=10 cm` `(` Convex `)` |
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| 343. |
The image of point `P` when viewed from top of the slabs will be A. `2.0cm` above `P`B. `1.5cm` above `P`C. `2.0 cm` below `P`D. `1 cm` above `P` |
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Answer» Correct Answer - D The two slabs will shift the image a distance `d=2(1+(1)/(mu))t=2(1-(1)/(1.5))(1.5)=1.0 cm` Therefore, final image will be `1 cm` above point `P`. |
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| 344. |
An ideal gas having initial pressure p, volume V and temperature T is allowed to expand adiabatically until its volume becomes 5.66V, while its temperature falls to `T//2`. (a) How many degrees of freedom do the gas molecules have? (b) Obtain the work done by the gas during the expansion as a function of the initial pressure p and volume V. Given that `(5.66)^0.4=2` |
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Answer» Correct Answer - `(i) f= 5 (ii) W = 12.3 PV` For polytropic process `T_(1)V_(1)^(n-1) = T_(2)V_(2)^(n-1) implies TV^(n-1) = (T)/(2)(5.66V)^(n-1) implies 2 = 5.66^(n-1)` Taking log both sides `ln2 = (n-1)ln 5.66` `implies n= 1.4 = 1 + (2)/(f) implies f=5` (i) `therefore` Degrees of freedom =`5` (ii) Work done by gas =`(P_(1)V_(1) - P_(2)V_(2))/(gamma-1) = (PV-P_(2)(5.66V))/(1.4-1) = 12.3PV` Where `P_(2)V_(2)^(gamma) = P_(1)V_(1)^(gamma) implies P_(2) = P((1)/(5.66))^(1//4)` |
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| 345. |
A potato gun first a potato horizontally down a half-open cylinder of cross-sectional area `A`. When the gun is fired , the potato slug is at rest , the volume betweeen the end of the cylinder and the potato is `V_(0)`, and the pressure of the gas in this volume is `P_(0)`. The atmospheric pressure is `P_("atm")`. where `P__(0) gt P_("atm")` . The gas in the cylinder is diatomic, this means that `C_(V) = (5R)/(2)` and `C_(P) = (7R)/(2)` . The potato moves down the cylinder quickly enough that no heat is transferred to the gas. Friction between the potato and the barreel is negligible and no gas leaks around the potato . The parameters `P_(0) , P_("atm"), V_(0)` and `A` are fixed, but the overall length `L` of the barrel may be varied. The length `L`in this case isA. `(V_(0))/(A) ((2P_(0))/(P_(atm)))^(5//7)`B. `(V_(0))/(A) ((P_(0))/(P_(atm)))^(5//7)`C. `(V_(0))/(2A) ((P_(0))/(P_(atm)))^(5//7)`D. `(2V_(0))/(A) ((P_(0))/(P_(atm)))` |
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Answer» Correct Answer - B `P_(0)V_(0)^(7//5) = P_(f)V_(f)^(7//5)` `V_(f) = AL` `W_(gas) + W_(atm) = DeltaKE` For `(KE)_(max) , (d(KE))/(dt) = 0` |
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| 346. |
A potato gun first a potato horizontally down a half-open cylinder of cross-sectional area `A`. When the gun is fired , the potato slug is at rest , the volume betweeen the end of the cylinder and the potato is `V_(0)`, and the pressure of the gas in this volume is `P_(0)`. The atmospheric pressure is `P_("atm")`. where `P__(0) gt P_("atm")` . The gas in the cylinder is diatomic, this means that `C_(V) = (5R)/(2)` and `C_(P) = (7R)/(2)` . The potato moves down the cylinder quickly enough that no heat is transferred to the gas. Friction between the potato and the barreel is negligible and no gas leaks around the potato . The parameters `P_(0) , P_("atm"), V_(0)` and `A` are fixed, but the overall length `L` of the barrel may be varied. The maximum kinetic energy `E_("max")` with which the potato can exit the barrel?A. `[(5)/(2)P_(0) + P_(atm) - (7)/(2)P_(atm)^(2//7)P_(0)^(5//7)]V_(0)`B. `[(5)/(2)P_(0) + P_(atm) - (5)/(2)P_(atm)^(2//7)P_(0)^(5//7)]V_(0)`C. `[(5)/(2)P_(0) + P_("atm")] V_(0)`D. `(5)/(2)(P_(0) + P_("atm")) V_(0)` |
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Answer» Correct Answer - A `P_(0)V_(0)^(7//5) = P_(f)V_(f)^(7//5)` `V_(f) = AL` `W_(gas) + W_(atm) = DeltaKE` For `(KE)_(max) , (d(KE))/(dt) = 0` |
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| 347. |
The efficiency of a heat engine is defined as the ratio of the mechanical work done by the engine in one cycle to the heat absorbed from the high temperature source . `eta = (W)/(Q_(1)) = (Q_(1) - Q_(2))/(Q_(1))` Cornot devised an ideal engine which is based on a reversible cycle of four operations in succession: isothermal expansion , adiabatic expansion. isothermal compression and adiabatic compression. For carnot cycle `(Q_(1))/(T_(1)) = (Q_(2))/(T_(2))`. Thus `eta = (Q_(1) - Q_(2))/(Q_(1)) = (T_(1) - T_(2))/(T_(1))` According to carnot theorem "No irreversible engine can have efficiency greater than carnot reversible engine working between same hot and cold reservoirs". An inventor claims to have developed an engine working between `600K` and `300K` capable of having an efficiency of `52%`, then -A. It is impossibleB. It is possibleC. It is nearly possibleD. Data is insufficient |
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Answer» Correct Answer - A `eta_(max) = (T_(1) -T_(2))/(T_(1)) xx 100 = (600-300)/(600) xx 100 = 50%` |
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| 348. |
A gas has volume `V` and pressure `p`. The total translational kinetic energy of all the molecules of the gas isA. `(3)/(2) PV` only if the gas is monoatomic.B. `(3)/(2) PV` only if the gas is diatomic.C. `gt(3)/(2) PV` if the gas is diatomic.D. `(3)/(2) PV` in all cases. |
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Answer» Correct Answer - D Total translational `KE` `(3)/(2)nRT = (3)/(2) PV` |
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| 349. |
As shown , a piston chamber pf cross section area `A` is filled with ideal gas. `A` sealed piston of mass m is right at the middle height of the cylinder at equilibrium. The friction force between the chamber wall and the piston can be ignored . The mass of the rest of the chamber is `M`.The atmosphere pressure is `P_(0)`. Now slowly pull the piston upwards , find the maximum value of `M` such that the chamber can be lifted off the ground. The temperature remains unchanged. A. ` M = (P_(0)A - 2mg)/(2g)`B. ` M = (P_(0)A - mg)/(2g)`C. ` M = (P_(0)A - mg)/(g)`D. ` M = (P_(0)A)/ (2g)` |
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Answer» Correct Answer - B `P_(f)V_(f) = P_(f)V_(f)` where `V_(L) = (V_(f))/(2)` |
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| 350. |
For a ideal monoatomic gas match the following graphs for constant mass in different processes (`rho` = Density of gas) |
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Answer» `P = (rho)/(M_(w))RT` For (A): For `AB P prop V implies T alphaV^(2) implies T prop rho^(-2)` For `BC V= "constant" implies rho = "constant"` For `CA P = "constant" implies rhoT = "constant"` For (B) For `AB P prop T implies rho = "constant"` For `BC T = "constant" implies P prop rho` For `CA P = "constant" implies rhoT = "constant"` For (C) For `AB P ="constant" implies rhoT = "constant"` For `BC T = "constant" implies P prop rho` For `CA V = "constant" implies rho = "constant"` For(D) For `AB rho prop T implies P prop T^(2)` For `BC T ="constant" implies P prop rho` For `A rho = "constant" implies P prop T` |
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