Thermodynamics JEE Main PYQs, 2020 to 2025

A monoatomic gas having $\gamma = \frac{5}{3}$ is stored in a thermally insulated container and the gas is suddenly compressed to $\left( \frac{1}{8} \right)^{\text{th}}$ of its initial volume. The ratio of final pressure and initial pressure is:

($\gamma$ is the ratio of specific heats of the gas at constant pressure and at constant volume)

The temperature of 1 mole of an ideal monoatomic gas is increased by $50^{\circ} \mathrm{C}$ at constant pressure. The total heat added and change in internal energy are $E_1$ and $E_2$, respectively. If $\frac{E_1}{E_2}=\frac{x}{9}$ then the value of $x$ is _________.

Water of mass $m$ gram is slowly heated to increase the temperature from $T_1$ to $T_\gamma$. The change in entropy of the water, given specific heat of water is $1 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}$, is :

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma=3 / 2$. The work done by the gas in the process is:

$(\mu=1 \text { mole })$

An engine operating between the boiling and freezing points of water will have

A. efficiency more than 27%.

B. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures.

C. efficiency equal to $27 \%$

D. efficiency less than $27 \%$

Choose the correct answer from the options given below: