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1.

A lead bullet penetrates into a solid object and melts. Assuming that 50% of its kinetic energy was used to heat it, calculate the initial speed of the bullet. The initial temperature of the bullet is `27^@C` and its melting point is `327^@C`. Latent heat of fusion of lead `= 2.5 xx 10^4 J//kg` and specific heat capacity of lead `=125 J//kg.K`.

Answer» Let the speed of bullet be `v`. The `50%` of kinetic energy is used in increasing the temperature from `27^@C` to `327^@C` and them melting the bullet.
`(1)/(2).(1)/(2)mv^2=msDeltatheta+mL_("fusion")`
`(v^2)/(4)=125xx(327-27)+2.5xx10^4`
`=3.75xx10^4+2.5xx10^4`
`v^2=4xx6.25xx10^4`
`v=2xx2.5xx10^2=500 m//s`
Discussion
2.

A lead bullet strikes against a steel plate with a velocity `200ms^-1`. If the impact is perfectly inelastic and the heat produced is equally shared between the bullet and the target, thent he rise in temperature of the bullet is (specific heat capacity of lead `=125Jkg^-1K^-1`)A. `80^@C`B. `60^@C`C. `160^@C`D. `40^@C`

Answer» Correct Answer - A
`(1)/(2)mv^2xx(1)/(2)=msDeltatheta`
`((200)^2)/(4)=125Deltatheta`
`Deltatheta=80^@C`
Discussion
3.

10 g of ice at `0^@C` is mixed with 100 g of water at `50^@C`. What is the resultant temperature of mixtureA. `31.2^@C`B. `32.8^@C`C. `36.8^@C`D. `38.2^@C`

Answer» Correct Answer - D
`100xxs_(omega)(50-theta)=10L_("ice")+10xx1xx(theta-0)`
`100xx1(50-theta)=10xx80+10theta`
`5000-1000=800+10theta`
`1100=4200`
`theta=38.2^@C`
Discussion
4.

19 g of water at `30^@C` and 5 g of ice at `-20^@C` are mixed together in a calorimeter. What is the final temperature of the mixture? Given specific heat of ice `=0.5calg^(-1) (.^(@)C)^(-1)` and latent heat of fusion of ice `=80calg^(-1)`A. `0^@C`B. `-5^@C`C. `5^@C`D. `10^@C`

Answer» Correct Answer - C
`19xx1xx(30-theta)=5xx0.5xx[0-(-20)]+5xx80+5xx1xx(theta-0)`
`570-19theta=50+400+5theta`
`240=120`
`theta=5^@C`
Discussion
5.

`1kg` ice at `0^(@)C` is mixed with `1kg` of steam at `100^(@)C`. What will be the composition of the system when thermal equilibrium is reached ? Latent heat of fusion of ice `= 3.36xx 10^(6)J kg^(-1)` and latent heat of vaporization of water `= 2.26 xx 10^(6)J kg^(-1)`

Answer» Heat released when 1 kg of steam is condensed.
`Q_1=mL_("steam")=1000xx540=540000cal`
Heat required to melt ice and increasing its temperature to `100^@C`
`Q_2=1000xx80+1000xx1xx(100-0)=180000`
At `Q_2 lt Q_1`, all of steam is not condensed, hence, equilibrium temperature is `100^@C` Let `m_0` is mass of steam condensed
`m_0xx540=Q_2=180000`
`m_0=333.3g`
Contents of mixture:
steam `1000-333.3=666.7g`
Water: `1000+333.3=1333.3g`
Discussion
6.

Four `2 cmxx2 cmxx 2cm` cubes of ice are taken from a refrigerator and put in `200ml` of a drink at `10^(@)C`(a) Find the temperature of the drink when thermal equilibrium is attained in it. (b) If the ice cubes do not melt completely, find the amount melted. Assume that no heat is lost to the outside of the drink and that the container has negligible heat capacity. Density of ice `= 900 kg m^(-8)` , density of the drink `= 1000kgm^(-8)`, specific heat capacity of the drink ` = 4200 J kg^(-1)K^(-1)` ,latent heat of fusion of ice `= 3.4 xx 10^(6)Jkg^(-1)`

Answer» Mass of cubes `=4xx0.9xx2xx2xx2=28.8g`
mass of drink `=1xx200=200g`
(a) Heat released by drinkwhen its temperature falls from `10^@C` to `0^@C`
`Q_1=200xx1xx(10-0)=2000cal`
Heat required to melt ice
`Q_2=28.8xx80=2304cal`
`Q_2 lt Q_1` whole of ice is not melted, hence, equilibrium temperature `=0^@C`
(b) Let `m` is mass of ice melted
`mxx80=Q_1=2000`
`m=25g`
Discussion
7.

A metallic ball and highly stretched spring are made of the same material and have the same mass. They are heated so that they melt. The latent heat requiredA. are the same for bothB. is greater for the ballC. is greater for the springD. for the two may or may not be the same depending upon the metal

Answer» Correct Answer - A
Discussion
8.

A liquid of mass m and specific heat c is heated to a temperature 2T. Another liquid of mass m/2 and specific heat 2 c is heated to a temperature T. If these two liquids are mixed, the resulting temperature of the mixture isA. `(2//3) T`B. `(8//5) T`C. `(3//5) T`D. `(3//2) T`

Answer» Correct Answer - D
Let equilibrium temperature be `theta`
`mC(2T-theta)=(m)/(2).2C(theta-T)`
`theta=(3T)/(2)`
Discussion
9.

Two liquids A and B are at `30^@C` and `20^@C`, respectively When they are mixied in equal masses, the temperature of the mixture is found to be `26^@C`. The ratio of their specific heat isA. `4:3`B. `3:4`C. `2:3`D. `3:2`

Answer» Correct Answer - D
`ms_A(30-26)=ms_B(26-20)`
`(s_A)/(s_B)=(6)/(4)=(3)/(2)`
Discussion
10.

A vessel contains `110 g` of water. The heat capacity of the vessel is equal to `10 g` of water. The initial temperature of water in vessel is `10^(@)C`. If `220 g` of ho, water at `70^(@)C` is poured in the vessel, the final temperature neglecting radiation loss, will beA. `70^@C`B. `80^@C`C. `60^@C`D. `50^@C`

Answer» Correct Answer - D
`220S(70-theta)=(110+10)s(theta-10)`
`11(70-theta)=6(theta-10)`
`770-110=60-60`
`170=830`
`thetacong50^@C`
Discussion
11.

When 300 J of heat is added to `25 gm` of sample of a material its temperature rises from `25^(@)C` to `45^(@)C`. The thermal capacity of the sample and specific heat of the material are respectively given by

Answer» `m=25g`,`Deltatheta=45-25=20^@C`,`DeltaQ=300J`
(a) Thermal capacity, `(DeltaQ)/(Deltatheta)=(300)/(20)=15J//.^(@)C`
(b) `ms=(DeltaQ)/(Deltatheta)`
`25xx10^-3s=1s`
Specific heat, `s=0.6xx10^3=600 J//Kg-^(@)C`
(c ) Number of holes `n=("mass")/("molecular mass")=(25)/(50)=(1)/(2)`
`DeltaQ=nCDeltatheta`
Molar heat capacity
`C=(DeltaQ)/(nDeltatheta)=(300)/((1//2)(20))=30J//"mole"^(@)C`
Discussion
12.

Steam at `100^@C` is allowed to pass into a vessel containing `10g` of ice and 100 g of water at `0^@C` until all the ice is melted and the temperature is raised to `50^@C`. Neglecting water equivalent of the vessel and the loss due to radiation etc. Calculate how much steam is condensed.

Answer» If `m` mass of steam,
`10xx80+(10+100)xx1xx(5-0)=mxx540+mxx1xx(100-5)`
`1350=635m`
`m=(1350)/(635)=2.12g`
Discussion
13.

The temperature of an object is observed to rise in a period. In this period (i) Heat is certainly supplied to it (ii) Heat is certainly not supplied to it (iii) heat may have been supplied to it (iv) work may have been done on it.A. (i),(iii)B. (ii),(iii)C. (iii),(iv)D. (i),(iv)

Answer» Correct Answer - C
Discussion
14.

Steam is passes into 22 g of water at `20^@C`. The mass of water that will be present when the water acquires a temperature of `90^@C` (Latent heat of steam is `540 cal//g`) isA. 24.8 gB. 24 gC. 36.6 gD. 30 g

Answer» Correct Answer - A
`mL_S+ms_(omega)(100-90)=22S_omega(90-20)`
`mxx540+mxx1xx10=22xx70`
`m=(22xx70)/(550)=2.8g`
Total mass of water `=22+2.8=24.8g`
Discussion
15.

1 kg of ice at `0^@C` is mixed with 1 kg of steam at `100^@C` (i) The equilibrium temperature is `100^@C` (ii) The equilibrium temperature is `0^@C` (iii) The contents of mixture are : 665 g steam, 1335 g water (iv) The contents of mixture are 800 g steam, 1200 g waterA. (i),(iii)B. (ii),(iii)C. (i),(iv)D. (ii),(iv)

Answer» Correct Answer - A
Discussion
16.

If heat is supplied to s solid its temperature (i) must increase (ii) may increase (iii) may remain same (iv) may decreaseA. (i),(iii)B. (ii),(iii)C. (iii),(iv)D. (i),(iv)

Answer» Correct Answer - B
Discussion
17.

Boiling water is changing into steam. Under this condition the specific heat of water isA. zeroB. oneC. infiniteD. less than one

Answer» Correct Answer - C
Discussion
18.

A solid material is supplied with heat at a constant rate. The temperature of the material is changing with heat input as shown (i) AB: change of state from solid to liquid. CD: change of state from liquid to vapour (ii) When `CD=2AB`, i.e., latent heat of vapourization is twice the latent heat of fusion of the substance. (iii) The reciprocal of slope of DE represents the heat capacity of vapour state of substance . (iv) If slope of `OAgt`slope of BC, i.e., specific heat of liquid state is greater than specific heat that of solid state.A. (i),(iii)B. (ii),(iii)C. (iii),(iv)D. (i),(iv)

Answer» Correct Answer - D
Discussion
19.

The temperature of equal masses of three different liquids A,B and C are `12^@C, 19^@C and 28^@C` respectively. The temperature when A and B are mixed is `16^@C` and when B and C are mixed it is `23^@C`. What should be the temperature when A and C are mixed?

Answer» Let specific heat of liquid A, B and C are `s_A`,`s_B` and `s_C` resprectively.
When A and B are mixed,
`ms_B(19-16)=ms_A(16-12)`
`3s_B=4s_Aimpliess_A=(3)/(4)s_B`
When B and C are mixed,
`ms_C(28-23)=ms_B(23-19)`
`5s_c=4s_Bimpliess_C=(4)/(5)s_B`
When A and C are mixed, let equilibrium temperature be `theta`
`ms_C(28-theta)=ms_A(theta-12)`
`(4)/(5)s_B(28-theta)=(3)/(4)s_B(theta-12)`
`16(28-theta)=15(theta-12)`
`448-16theta=15theta-180`
`31theta=628`
`theta=(628)/(31)=20.3^@C`
Discussion