Q. An ideal gas is allowed to expand freely against vacuum in a rigid insulated container. The gas undergoes :

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A

An increase in its internal energy

B

A decrease in its internal energy

C

Neither an increase or decrease in temperature or internal energy

D

An increase in temperature

Solution:

Expansion of a gas in vaccum is free expansion in which no work is done and as container is insulated, no heat supply will take place so no change in internal energy of gas will occur.

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1. The concept of temperature in thermodynamics is suggested by the

2. 1 g of water is evaporated at 1 atmospheric pressure. Its volume in liquid phase is $1 \,cm ^{3}$ which becomes $1671 \,cm ^{3}$ in the vapour phase. If the latent heat of water is $2256 \,J / g $, then change in its internal energy is

3. One mole of an ideal gas at temperature $T$ was cooled isochorically till the gas pressure fell from $P$ to $\frac{P}{n}$. Then, by an isobaric process, the gas was restored to the initial temperature. The net amount of heat absorbed by the gas in the process is

4. Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and same volume $V$. The mass of the gas in $A$ is $m_{A}$ and that in $B$ is $m_{B}$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2 V$. The changes in the pressure in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$ respectively. Then

5. An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cros section $8.0 \times 10^{-3} \, m^2$. Initially the gas is at 300K and occupies a volume of $2.4 \times 10^{-3} \, m^3$ and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by $0.1\, m$. The force constant of the spring is $8000\, N/m$ and the atmospheric pressure is $1.0 \times 10^5 \, N/m^2$. The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be :
(Neglect the heat loss through the lead wires of the heater. The heat capacity of the heater coil is also negligible)

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