Heat & Thermodynamics · JEE Main previous year questions

If minimum possible work is done by a refrigerator in converting 100 grams of water at $0^{\circ }\mathrm{C}$ to ice, how much heat (in calories) is released to the surroundings at temperature $27^{\circ }\mathrm{C}$ (Latent heat of ice = 80 Cal/gram) to the nearest integer ?

An engine takes in 5 moles of air at $20^{\circ }\mathrm{C}$ and $1\mathrm{atm}$, and compresses it adiabatically to $1/10^{\mathrm{th}}$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be $X\mathrm{kJ}$. The value of $X$ to the nearest integer is ____.

A heat engine is involved with exchange of heat of 1915 J, – 40J, + 125 J and –Q J, during one cycle achieving an efficiency of 50.0%. The value of Q is

1. A.980 J
2. B.40 J
3. C.400 J
4. D.640 J

Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass $\frac{m}{4}$. The ratio of the specific heats ($C_V^A$ and $C_V^B$) of gas A and B, respectively is :

1. A.$7:9$
2. B.$5:7$
3. C.$3:5$
4. D.$5:9$

1. A.
2. B.
3. C.
4. D.

Starting at temperature 300 K, one mole of an ideal diatomic gas ($\gamma =1.4$) is first compressed adiabatically from volume ${\mathrm{V}}_1$ to ${\mathrm{V}}_2=\frac{{\mathrm{V}}_1}{16}$. It is then allowed to expand isobarically to volume $2{\mathrm{V}}_2$. If all the processes are the quasi-static then the final temperature of the gas (in ${}^{\circ }\mathrm{K}$) is (to the nearest integer) _______.

1. A.
2. B.
3. C.
4. D.

Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its ${\mathrm{C}}_{\mathrm{p}}/{\mathrm{C}}_{\mathrm{v}}$ value will be :

1. A.23/15
2. B.67/45
3. C.40/27
4. D.19/13

A carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at lower temperature is :

1. A.90 J
2. B.99 J
3. C.1 J
4. D.100 J

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $\gamma =1.40$, the work done by air is : ($3^{1.4}=4.6555$) [Take air to be an ideal gas]

1. A.$60.7\mathrm{J}$
2. B.$100.8\mathrm{J}$
3. C.$90.5\mathrm{J}$
4. D.$48\mathrm{J}$

A Carnot engine operates between two reservoirs of temperatures 900 K and 300 K. The engine performs 1200 J of work per cycle. The heat energy (in J) delivered by the engine to the low temperature reservoir, in a cycle, is _______.

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from ${\tau }_1$ to ${\tau }_2$. If $\frac{C_p}{C_v}=\gamma$ for this gas then a good estimate for $\frac{{\tau }_2}{{\tau }_1}$ is given by :

1. A.$(2{)}^{\frac{1+\gamma }{2}}$
2. B.2
3. C.${\left(\frac{1}{2}\right)}^{\frac{1+\gamma }{2}}$
4. D.${\left(\frac{1}{2}\right)}^{\gamma }$

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperature, $T_1$ and $T_2$. The temperature of the hot reservoir of the first engine is $T_1$ and the temperature of the cold reservoir of the second engine is $T_2$. T is temperature of the sink of first engine which is also the source for the second engine. How is T related to $T_1$ and $T_2$, if both engines perform equal amount of work?

1. A.$T=\frac{2T_1{T}_2}{T_1+T_2}$
2. B.$T=\sqrt{T_1{T}_2}$
3. C.$T=\frac{T_1+T_2}{2}$
4. D.$T=0$

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ? (R = 8.3 J/mol K)

1. A.21.6 J/mol K
2. B.17.4 J/mol K
3. C.15.7 J/mol K
4. D.19.7 J/mol K

When $M_1$ gram of ice at $-10^{\circ }\text{C}$ (specific heat = $0.5{\text{ cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$) is added to $M_2$ gram of water at $50^{\circ }\text{C}$, finally no ice is left and the water is at $0^{\circ }\text{C}$. The value of latent heat of ice, in ${\text{cal g}}^{-1}$ is :

1. A.$\frac{50M_2}{M_1}-5$
2. B.$\frac{50M_2}{M_1}$
3. C.$\frac{5M_2}{M_1}-5$
4. D.$\frac{5M_1}{M_2}-50$

One kg of water, at $20^{\circ }\text{C}$, heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of $20\Omega$. The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time taken for water to evaporate fully, is close to : [Specific heat of water = $4200{\text{ J/(kg }}^{\circ }\text{C)}$, Latent heat of water = $2260\text{ kJ/kg}$]

1. A.10 minutes
2. B.22 minutes
3. C.3 minutes
4. D.16 minutes

A Carnot engine has an efficiency of $\frac{1}{6}$. When the temperature of the sink is reduced by $62^{\circ }\text{C}$, its efficiency is doubled. The temperatures of the source and the sink are, respectively

1. A.$99^{\circ }\text{C},37^{\circ }\text{C}$
2. B.$124^{\circ }\text{C},62^{\circ }\text{C}$
3. C.$37^{\circ }\text{C},99^{\circ }\text{C}$
4. D.$62^{\circ }\text{C},124^{\circ }\text{C}$

n moles of an ideal gas with constant volume heat capcity ${\mathrm{C}}_{\mathrm{V}}$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is :

1. A.$\frac{nR}{C_V-nR}$
2. B.$\frac{4nR}{C_V-nR}$
3. C.$\frac{4nR}{C_V+nR}$
4. D.$\frac{nR}{C_V+nR}$

A massless spring (k = 800 N/m), attached with a mass (500 g) is completely immersed in 1 kg of water. The spring is stretched by 2 cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely ? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4184 J/kg K)

1. A.$10^{-3}\mathrm{K}$
2. B.$10^{-1}\mathrm{K}$
3. C.$10^{-5}\mathrm{K}$
4. D.$10^{-4}\mathrm{K}$

The specific heats, ${\mathrm{C}}_{\mathrm{p}}$ and ${\mathrm{C}}_{\mathrm{v}}$ of a gas of diatomic molecules, A, are given (in units of $\mathrm{J}\mathrm{mo}{\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :-

1. A.A is rigid but B has a vibrational mode
2. B.A has a vibrational mode but B has none
3. C.A has one vibrational mode and B has two
4. D.Both A and B have a vibrational mode each

1. A.$\frac{{\theta }_1}{10}+\frac{9{\theta }_2}{10}$
2. B.$\frac{{\theta }_2+{\theta }_1}{2}$
3. C.$\frac{{\theta }_1}{6}+\frac{5{\theta }_2}{6}$
4. D.$\frac{{\theta }_1}{3}+\frac{2{\theta }_2}{3}$

In a conductor, if the number of conduction electrons per unit volume is $8.5\times 10^{28}{\mathrm{m}}^{-3}$ and mean free time is 25fs (femto second), it's approximate resistivity is :- (${\mathrm{m}}_{\mathrm{e}}=9.1\times 10^{-31}\mathrm{kg}$)

1. A.$10^{-8}\Omega \mathrm{m}$
2. B.$10^{-7}\Omega \mathrm{m}$
3. C.$10^{-5}\Omega \mathrm{m}$
4. D.$10^{-6}\Omega \mathrm{m}$

1. A.d a b c
2. B.a d b c
3. C.d a c b
4. D.a d c b

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is $K_1$ and the of the outer cylinder is $K_2$. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is :

1. A.$K_1+K_2$
2. B.$\frac{K_1+3K_2}{4}$
3. C.$\frac{K_1+K_2}{2}$
4. D.$\frac{2K_1+3K_2}{5}$

A metal ball of mass $0.1\text{ kg}$ is heated upto $500^{\circ }\mathrm{C}$ and dropped into a vessel of heat capacity $800{\text{ JK}}^{-1}$ and containing $0.5\text{ kg}$ water. The initial temperature of water and vessel is $30^{\circ }\mathrm{C}$. What is the approximate percentage increment in the temperature of the water? [Specific Heat Capacities of water and metal are, respectively, $4200{\text{ Jkg}}^{-1}{\text{K}}^{-1}$ and $400{\text{ Jkg}}^{-1}{\text{K}}^{-1}$]

1. A.20%
2. B.25%
3. C.15%
4. D.30%