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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.
| 1. |
Calculate the value of `gamma` for a gaseous mixture consisting `n_(1)` moles of oxygen and `n_(2)` moles of carbon dioxide. The values of `gamma` for oxygen and carbon dioxide are `gamma_(1)` and `gamma_(2)` respectively. Assume the gases to be ideal. |
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Answer» Correct Answer - `gamma=(gamma_(1)gamma_(2)(n_(1)+n_(2))-(n_(1)gamma_(1)+n_(2)gamma_(2)))/(n_(1)(gamma_(2)-1)+n_(2)(gamma_(1)-1))` |
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| 2. |
One mole of a gas is in state `A[P, V, T_(A)]`. A small adiabatic process causes the state of the gas to change to `B [P + dP, V + dV, T_(B)]`. The changes dV & dP are infinitesimally small and dV is negative. An alternative process takes the gas from state A to B via `A rarr C rarr B`. `A rarr C` is isochoric and `C rarr B` is isobaric path. State at C is `[P + dP, V, T_(C)]`. (a) Rank the temperatures `T_(A), T_(B)` and `T_(C)` from highest to lowest. (b) Find g of the gas in terms of `T_(A)`, `T_(B)` and `T_(C)`. |
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Answer» Correct Answer - (a) `T_(C) gt T_(B) gt T_(A)` , (b) `gamma = (T_(C)-T_(A))/(T_(C)-T_(B))` |
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| 3. |
A bullet of lead melts when stopped by obstacle. Assuming that 25 per cent of the heat is absorbed by the osbtacle, find the velocity of the bullet if its initial temperature is `27^(@)C`. (Melting point of lead `327^(@)C`, specific heat capacity of lead `=30 cal kg^(-1)K^(-1)` specific latent heat of fusion of lead `=6000 cal kg^(-1)` and `J=4.2` joules `cal^(-1)`) |
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Answer» Correct Answer - `410ms^(-1)` |
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| 4. |
Calculate the amount of heat required in calorie to change 1 g of ice at `-10^(@)C` to steam at `120^(@)C`. The entire process is carried out at atmospheric pressure. Specific heat of ice and water are `0.5 cal g^(-1) .^(@)C^(-1)` and `1.0 cal g^(-1) .^(@)C^(-1)` respectively. Latent heat of fusion of ice and vaporization of water are `80 cal g^(-1)` and `540 cal g^(-1)` respectively. Assume steam to be an ideal gas with its molecules having 6 degrees of freedom. Gas constant `R = 2 cal mol^(-1) K^(-1)`. |
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Answer» Correct Answer - 733.8 cal |
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| 5. |
A gas-gun has a cylindrical bore made in an insulating material. Length of the bore is L. A small bullet having mass m just fits inside the bore and can move frictionlessly inside it. Initially n moles of helium gas is filled in the bore to a length `L_(0)`. The bullet does not allow the gas to leak and the bullet itself is kept at rest by a stopper S. The gas is at temperature `T_(0)`. The gun fires if the stopper S is removed suddenly. Neglect atmospheric pressure in your calculations [Think that the gun is in space]. (a) Calculate the speed with which the bullet is ejected from the gun. (b) Find the maximum possible speed that can be imparted to the bullet by using n moles of helium at temperature `T_(0)`. |
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Answer» Correct Answer - (a) `u = sqrt((3nRT_(0))/(m)[1-((L_(0))/(L))^(2//3)])` (b) `u_(max) = sqrt((3nRT_(0))/(m))` |
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| 6. |
A spherical container made of non conducting wall has a small orifice in it. Initially air is filled in it at atmospheric pressure `(P_(0))` and atmospheric temperature `(T_(0))`. Using a small heater, heat is slowly supplied to the air inside the container at a constant rate of H J/s. Assuming air to be an ideal diatomic gas find its temperature as a function of time inside the container. |
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Answer» Correct Answer - `T=T_(0)e^((2Ht)/(7n_(0)T_(0)R))` |
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| 7. |
A tube of length `2m` containing a little mercury and closed at both ends is rapidly inverted 50 times. What is the maximum rise in temperature expected? (Specific heat capacity of mercury `=30calkg^(-1) K^(-1)` and `J=4.2` joules//cal.) |
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Answer» Correct Answer - `7.78^(@)C` |
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| 8. |
Air is filled inside a jar which has a pressure gauge connected to it. The temperature of the air inside the jar is same as outside temperature `(= T_(0))` but pressure `(P_(1))` is slightly larger than the atmospheric pressure `(P_(0))`. The stopcock is quickly opened and quickly closed, so that the pressure inside the jar becomes equal to the atmospheric pressure `P_(0)`. The jar is now allowed to slowly warm up to its original temperature `T_(0)`. At this time the pressure of the air inside is `P_(2) (P_(0) lt P_(2) lt P_(1))`. Assume air to be an ideal gas. Calculate the ratio of specific heats `(= gamma)` for the air, in terms of `P_(0), P_(1)` and `P_(2)`. |
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Answer» Correct Answer - `gamma = (ln(P_(0)//P_(1)))/(ln(P_(2)//P_(1)))` |
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| 9. |
A sample of oxygen is heated in a process for which the molar specific heat capacity is 2R. During the process the temperature becomes `(32)^(1//3)` times of the original temperature. How does the volume of the gas change? |
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Answer» Correct Answer - Volume doubles |
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| 10. |
An ideal diatomic gas undergoes a process in which the pressure is proportional to the volume. Calculate the molar specific heat capacity of the gas for the process. |
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Answer» Correct Answer - `3R` |
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| 11. |
A glass tube is inverted and dipped in mercury as shown. One mole of an ideal monoatomic gas is trapped in the tube and the tube is held so that length of the tube above the mercury level is always `h_(0)` meter. The atmospheric pressure is equal to `h_(0)` meter of mercury. The mercury vapour pressure, heat capacity of mercury, tube and the container are negligible. How much heat must be supplied to the gas inside the tube so as to increase its temperature by `Delta T`? |
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Answer» Correct Answer - `2RDeltaT` |
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| 12. |
The molar specific heat capacity at constant volume `(C_(V))` for an ideal gas changes with temperature as shown in the graph. Find the amount of heat supplied at constant pressure in raising the temperature of one mole of the gas from 200 K to 400 K. |
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Answer» Correct Answer - `706.25 R` |
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| 13. |
Three moles of an ideal gas, initially at `T_(0)=273K` isothermally expanded `n=5` times its initial volume and then isochorically heated so that the pressure in the final state became equal to that in the initial state. The total quantity of heat transferred to the gas during the process was `Q=80kJ`. Represent the whole process in a `pV` diagram. Find the adiabatic exponent of the gas. |
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Answer» Correct Answer - `1.4` |
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| 14. |
An adiabatic cylindrical chamber with a frictionless movable piston has been placed on a smooth horizontal surface as shown. One mole an ideal monotonic gas is enclosed inside the chamber. Mass of the piston is M and mass of the remaining chamber including the gas is 4 M. The gas is at atmospheric pressure and temperature. A particle of mass M moving horizontally with speed v, strikes the piston elastically. Find the change in temperature of the gas when the compression is maximum. |
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Answer» Correct Answer - `(4Mv^(2))/(15R)` |
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| 15. |
A cylindrical container has insulating wall and an insulating piston which can freely move up and down without any friction. It contains a mixture of ideal gases. Originally the gas is at atmospheric pressure `P_(0)` and temperature `(T_(0))`. A tap positioned above the container is opened and it supplies water at a constant rate of `(dm)/(dt)= 0.25 kg//s`. The water collects above the piston in the container and the gas compresses. The tap is kept open till the temperature of the gas is doubled. During the process the T vs `(1)/(V)` graph for the gas was recorded and found to be a parabola with its vertex at origin as shown in the graph. Area of piston `A = 1.515 xx 10^(-3) m^(2)` and atmospheric pressure `= 10^(5) N//m^(2)` (a) Find the ratio of `V_(rms)` and speed of sound in the gaseous mixture. (b) For how much time the tap was kept open? |
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Answer» Correct Answer - (a) `sqrt(2)` (b) 290 second |
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| 16. |
(i) An adiabatic cylinder contains an ideal gas. It is fitted with a freely movable insulating piston. In one experiment the piston is pulled out very fast to double the volume of the gas. In another experiment starting from same initial state, the piston is pulled out very slowly to double the volume of the gas. At the end of which experiment the final pressure of the gas will be higher? (ii) An ideal gas is contained in a cylinder fitted with a movable piston. In an experiment ‘A’ the gas is allowed to perform a work `W (gt 0)` on the surrounding during an isobaric process and thereafter the pressure of the gas is reduced isochorically to half the initial value. At the end of the experiment the temperature of the gas is `T_(A)`. In a different experiment ‘B’ the pressure of the gas is reduced to half in an isochoric process and then the gas performs a work W on the surrounding during an isobaric process. At the end of the experiment the gas temperature is `T_(B)`. Which is higher, `T_(A)` or `T_(B)`? |
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Answer» Correct Answer - (i) Experiment 1 , (ii) `T_(B)` |
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| 17. |
An adiabatic cylinder has length 2 L and cross sectional area A. A freely moving non conducting piston of negligible thickness divides the cylinder into two equal parts. The piston is connected to the right face of the cylinder with an ideal spring of force constant k. The right chamber contains 28 g nitrogen in which one third of the molecules are dissociated into atoms. The left chamber container 4 g helium. With piston in equilibrium and spring relaxed the pressure in both chamber is `P_(0)`. The helium chamber is slowly given heat using an electric heater (H), till the piston moves to right by a distance `(3L)/(4)`. Neglect the volume occupied by the spring and the heating coil. Also neglect heat capacity of the spring. (a) Find the ratio of `C_(P)` and `C_(V)` for nitrogen gas in right chamber. (b) Calculate change in temperature of helium. (c) Calculate heat supplied by the heater. |
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Answer» Correct Answer - `(a) gamma=3/2 " " (b) 1/R[(15 kL^(2))/16+9P_(0)Al]` (c) `2/16 kL^(2)+35/2 P_(0)Al` |
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| 18. |
An adiabatic cylinder of cross section A is fitted with a mass less conducting piston of thickness d and thermal conductivity K. Initially, a monatomic gas at temperature `T_(0)` and pressure `P_(0)` occupies a volume `V_(0)` in the cylinder. The atmospheric pressure is `P_(0)` and the atmospheric temperature is `T_(1) (gt T_(0))`. Find (a) the temperature of the gas as a function of time (b) the height raised by the piston as a function of time. Neglect friction and heat capacities of the container and the piston. |
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Answer» Correct Answer - (a) `T=T_(1)-(T_(1)-T_(0))e^(-betat)` `(b) Delta h=(V_(0)(T_(1)-T_(0))/(AT_(0))[1-e^(-betat)]` where `beta=(2T_(0)KA)/(5P_(0)V_(0)d)` |
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| 19. |
Find how much heat is necesssary to do internal work in converting `1g` of water at the normal boiling point into steam at the same temperature. Latent heat capacity of steam `=540xx10^(3)calkg^(-1)`, volume of `1kg` of steam at `100^(@)C=1.65m^(3)` |
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Answer» Correct Answer - `500cal` |
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| 20. |
How much heat must be supplied to nitrogen in a process of heating at constant pressure that the gas may perform 2 joules of work? |
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Answer» Correct Answer - `7J` |
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| 21. |
How much work is needed to convert `5g` of ice at `-3^(@)C` to steam at `100^(@)C`? (Sp. Heat capacity of ice `=500 cal kg^(-1)K^(-1)` sp. Latent heat of fusion of ice `=80xx10^(3) cal kg^(-1)` sp. Latent heat of vaporization of water `=536xx10^(3)calkg^(-1)`, and `J=4.2` joules per calorie) |
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Answer» Correct Answer - `15067.5J` |
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| 22. |
There is a long vertical tube of radius r containing air at atmospheric pressure. A steel ball is held at the mouth of the tube and dropped. The ball has radius r and it just fits inside the tube. The tube wall is perfectly smooth and no air can leak from the tube as the ball falls inside it. The ball falls through half the length of the tube before coming to rest. Assume that wall of the tube is perfectly conducting and temperature of the air inside the tube remains constant. Density of steel is d and atmospheric pressure is `P_(0)` and take `L gt gt r`. Take air to be an ideal gas. (a) Find the radius (r) of the tube. (b) At what depth from the top of the tube the ball will be in equilibrium? |
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Answer» Correct Answer - (a) `r=3/2 ln (2) (P_(0))/(dg) " " (b) L[1-1/(2ln(2))]` |
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| 23. |
Helum gas is used as working substance in an engine working on a thermodynamic cycle A – B – C – D – A. Process AB is isobaric, BC is adiabatic compression. During process CD, pressure is increased keeping the volume constant and DA is an isothermal process. The gas has maximum volume at A and the ratio of maximum to minimum volume during the entire cycle is `8sqrt(2)` . Also, the ratio of maximum to minimum absolute temperature is 4. (a) Represent the cycle on a P – V diagram. (b) Calculate efficiency of the cycle in percentage if it is used as an engine. [Take ln 2 = 0.693] |
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Answer» Correct Answer - (b) 41% |
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| 24. |
One mole of a mono atomic gas of molar mass M undergoes a cyclic process as shown in the figure. Here `rho` is density and P is pressure of the gas. (a) Calculate the heat rejected by the gas in one complete cycle. (b) Find the efficiency of the cycle. |
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Answer» Correct Answer - `(a) (P_(0)M)/(rho_(0)) (3/2+ln2) " " (b) 2/5 (1-ln2)` |
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| 25. |
One mole of an ideal monoatomic gas is taken through a cycle a-b-c-a as shown in figure. Find the difference in maximum and minimum value of internal energy of the gas during the cycle |
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Answer» Correct Answer - `(9)/(2)P_(0)V_(0)` |
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| 26. |
A ball of radius r fits tightly inside a tube attached to a container. There is no friction between the tube wall and the ball. Volume of air inside the container is `V_(0)` when the ball is in equilibrium. Density of the material of the ball is d and atmospheric pressure is `P_(0)`. If the ball is displaced a little from its equilibrium position and released, find time period of its oscillation. Assume that temperature in the container remains constant and that air is an ideal gas. |
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Answer» Correct Answer - `T=4sqrt((piV_(0)d)/(3P_(0)r))` |
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| 27. |
One end of an insulating U tube is sealed using insulating material. A mono atomic gas at temperature 300 K occupies 20 cm length of the tube as shown. The level of mercury on two sides of the tube differ by 5 cm. The other end of the tube is open to atmosphere. Area of cross section of the tube is uniform and is equal to `0.01 m^(2)`. The gas in the tube is heated by an electric heater so as to raise its temperature to 562.5 K. Assume that no heat is conducted to mercury by the gas. (a) Find the final length of the gas column. (b) Find the amount of heat supplied by the heater to the gas. |
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Answer» Correct Answer - (a) `30 cm` , (b) `406 J` |
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| 28. |
In the shown figure curve 1 represents an adiabat for n moles of an ideal mono atomic gas. Curve 2 and 3 are two isotherms for the same sample of the gas. Calculate the ratio of work done by the gas in doubling its volume from V to 2V along the isotherms 2 and 3. |
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Answer» Correct Answer - `(W_(1))/(W_(2)) = 2^(2//3)` |
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| 29. |
A system undregoes a change of state during which `100kJ` of heat is transferred to it and it does `50kJ` of work. The system is brought back to its original state through a process during which `120kJ` of heat is transferred to it. Find the work done by the system in the second process. |
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Answer» Correct Answer - `170kJ` |
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| 30. |
An ideal gas is taken through cycle 1231 (see figure) and the efficiency of the cycle was found to be 25%. When the same gas goes through the cycle 1341 the efficiency is 10%. Find the efficiency of the cycle 12341. |
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Answer» Correct Answer - 0.325 |
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| 31. |
A hole is drilled into a block of lead of mass `10kg` by a driller. The driller is driven by an electric motor of 30 r.p.m. and the couple exerted by the motor on the driller is `10Nm`. Calculate the rise in temperature of the lead in 10 minutes. `J=4.2` joules `cal^(-1)`. Relative specific heat capacity of lead 0.03 and sp. heat capacity of water `1000 cal kg^(-1)K^(-1)`. |
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Answer» Correct Answer - `14.96^(@)C` |
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| 32. |
Two lead spheres of masses `10kg` and `30k` approach each other with speeds `10ms^(-1)` and `20ms^(-1)` and collide completely inelastically. What is the heat produced by the collision? What is the rise in temperature if all the heat produced is ratained by the spheres? (Specific heat capacity of lead `=31 cal kg^(-1)K^(-1)` and `J=4.2` joules `cal^(-1)`) |
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Answer» Correct Answer - `3375J,0.65^(@)C` |
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| 33. |
`20g` of water is enclosed in a thermally insulated cylinder at a temperature of `0^(@)C` under a weightless piston whose area is `s=500cm^(2)`. The outside pressure is equal to standard atmospheric pressure. To what height will the piston rise when water absorbs `Q=20kJ` of heat? Sp. heat of water `=4200J//kg//K`, sp. latent heat of water `=2250kJ//kg` and boiling point of water `=373K` |
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Answer» Correct Answer - `16.4cm` |
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| 34. |
A thermally insulated vessel containing a gas, whose molar mas is equal to `M` and specific heat capacity ratio `gamma`, moves with a velocity `V`. Find the temperature rise when the vessel is stopped suddenly. |
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Answer» Correct Answer - `1//2Mv^(2)(gamma-1)//R` |
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| 35. |
The average number of degree of freedom per molecule for a gas is 7. A sample of the gas perform 30 J of work when it expands at constant pressure. Find the heat absorbed by the gas in the process. |
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Answer» Correct Answer - 135 J |
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| 36. |
A mole of an ideal gas initially at a temperature `T_(1)=290K` expands isobarically until its volume increases 2 times. Next the gas is cooled isochorically to its initial temperature `T_(1)`.Find (a) the incement `DeltaU` in the internal energy of the gas, (b) the work `A` done by the gas (c) the amount of the heat `Q` received by the gas. |
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Answer» Correct Answer - (a) 0 (b) `2.4kJ`, (c) `2.4kJ` |
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| 37. |
An ideal gas, in initial state 1`(P_(1), V_(1), T_(1))` is cooled to a state 3`(P_(3), V_(3), T_(3))` by a process which can be represented by a straight one on the P–V graph. The same gas in a different initial state 2 `(P_(2), V_(2), T_(1))` is cooled to same final state 3 `(P_(3), V_(3), T_(3))` by a process which can also be represented by a straight line on the same P–V graph. `Q_(1)` and `Q_(2)` are heat rejected by the gas in the two processes. Which is larger `Q_(1)` or `Q_(2)`. It is given that `P_(1) gt P_(2). |
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Answer» Correct Answer - `Q_(2) gt Q_(1)` |
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| 38. |
For an ideal gas the ratio of specific heats is `(C_(p))/(C_(v)) = gamma`. The gas undergoes a polytropic process PV^(n) =` a constant. Find the values of n for which the temperature of the gas increases when it rejects heat to the surrounding. |
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Answer» Correct Answer - `1 lt n lt gamma` |
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| 39. |
Two tanks are connected by a valve. One tank contains 2 kg of an ideal gas at `77^(@)C` and 0.7 atm pressure. The other tank has 8kg of same gas at `27^(@)C` and 1.2 atm pressure. The valve is opened and the gases are allowed to mix. The final equilibrium temperature was found to be `42^(@)C`. (a) Find the equilibrium pressure in both tanks. (b) How much heat was transferred from surrounding to the tanks during the mixing process. Given: `C_(v)` for the gas is `0.745 KJ kg^(-1) K^(-1)`. |
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Answer» Correct Answer - (a) `1.05 atm` , (b) `37.25 KJ` |
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| 40. |
An ideal gas undergoes a series of processes represented by`a rarr B rarr C rarr D` on the P-V diagram. Answer the following questions. (a) Is the internal energy of the gas at B and D equal? (b) Find work done by the gas in the process A rarr B rarr C rarr D`. (c) Is it right to say that point B and D lie on an isotherm? (d) Find the ratio of internal energy of the gas in state A to that in state D. |
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Answer» Correct Answer - (a) Yes , (b) `-(3)/(2)P_(0)V_(0)` (c) Yes , (d) `2 :1` |
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| 41. |
The ratio of specific heats (`C_(p)` and `C_(v)`) for an ideal gas is `gamma`. Volume of one mole sample of the gas is varied according to the law `V = (a)/(T^(2))` where T is temperature and a is a constant. Find the heat absorbed by the gas if its temperature changes by `Delta T`. |
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Answer» Correct Answer - `Delta Q = R((3-2 gamma)/(gamma-1))Delta T` |
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| 42. |
n moles of an ideal mono atomic gas is initially at pressure `32 P_(0)` and volume `V_(0)`. Its volume is doubled by an isobaric process. After this the gas is adiabatically expanded so as to make its volume `16V_(0)`. Now the gas is isobarically expanded. Finally, the gas is made to return to its initial state by an isothermal process. (a) Represent the process on a P–V diagram. (b) Calculate work done by the gas in one cycle. |
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Answer» Correct Answer - (b) `W = 8 P_(0)V_(0)` |
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| 43. |
A Carnot cycle based ideal heat engine operates between two tanks each having same mass m of water. The source tank has an initial temperature of `T_(1) = 361 K` and the sink tank has an initial temperature of `T_(2) = 289 K`. Assume that the two tanks are isolated from the surrounding and exchange heat with the engine only. Specific heat of water is s. (a) Find the final common temperature of the two tanks. (b) Find the total work that the engine will be able to deliver by the time the two tanks reach common temperature. |
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Answer» Correct Answer - (a) `T_(0)=sqrt(T_(1)T_(2))=323 K` (b) W=ms `(T_(1)+T_(2)-2sqrt(T_(1)T_(2)) =4ms ` |
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| 44. |
A room air conditioner is a Carnot cycle based heat engine run is reverse. An amount of heat `Q_(2)` is absorbed from the room at a temperature `T_(2)` into coils having a working gas (these gases are not good for environment!). The gas is compressed adiabatically to the outside temperature `T_(1)`. Then the gas is compressed isothermally in the unit outside the room, giving off an amount of heat `Q_(1)`. The gas expands adiabatically back to the temperature`T_(2)` and the cycle is repeated. The electric motor electric consumes power P. (i) Find the maximum rate at which heat can be removed from the room. (i) Heat flows into the room at a constant rate of `k DeltaT` where k is a constant and `Delta T` is temperature difference between the outside and inside of the room. Find the smallest possible room temperature in terms of `T_(1), k` and P. |
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Answer» Correct Answer - `(i) P((T_(2))/(T_(1)-T_(2)))` `(ii) T_(1)-P/k [sqrt(1+(4kT_(1))-1]` |
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| 45. |
The figure shows a Carnot cycle for an ideal gas on a P-V diagram. Which of the areas `A_(1)` or `A_(2)` is larger? |
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Answer» Correct Answer - `A_(1) = A_(2)` |
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| 46. |
An ideal gas is taken from its initial state a to its find state d in three different quasi static processes marked as a – b – d, a – o – d and a – c – d. Rank the net heat absorbed by the gas in the three processes. The diagram shown is a circle with centre at o. |
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Answer» Correct Answer - `Delta Q_("abd") gt Delta Q_("aod") gt Delta Q_("acd")` |
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| 47. |
An ideal mono atomic gas is at temperature `T_(0)`. The pressure and volume are quasi-statically doubled such that the process traces a straight line on the PV diagram. (a) Calculate the heat absorbed by the gas in the process if number of moles of the gas in the sample is n. (b) Calculate the average molar specific heat capacity of the gas for the process. |
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Answer» Correct Answer - `(a) Delta Q =6nRT_(0)" " (b) 2R` |
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| 48. |
30 people gather in a 1`0 m xx 5 m xx 3 m` room for a confidential meeting. The room is completely sealed off and insulated. Calculate the rise in temperature of the room in half an hour. Assume that average energy thrown off by the body of a person is 2500 kcal/day, density of air is `1.2 kg/m^(3)` and specific heat specify capacity of air at constant volume is `0.24 k cal kg^(-1) . ^(@)C^(-1)`. Neglect volume occupied by human bodies. |
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Answer» Correct Answer - `36^(@)C` |
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| 49. |
One mole of an ideal gas is carried through a thermodynamics cycle as shown in the figure. The cycle consists of an isochoric, an isothermal and an adiabatic process. Find the adiabatic exponent of the gas. |
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Answer» Correct Answer - `gamma = (ln6)/(ln3)` |
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