IAT (IISER) 2024 | Heat and Thermodynamics Question 1 | Physics

One mole of an ideal gas of volume $V$ and temperature $T$ is allowed to expand adiabatically to volume $2 V$ while doing no external work. The universal gas constant is $R$. What is the pressure of the gas after expansion?

$\frac{R T}{V}$

$\frac{R T}{2 V}$

$\frac{2 R T}{V}$

$\frac{R T}{4 V}$

IAT (IISER) 2024

MCQ (Single Correct Answer)

-1

Two identical boxes contain the same ideal gas. Let $\left(n_1, \lambda_1, T_1\right)$ and $\left(n_2, \lambda_2, T_2\right)$ be the number density, mean free path and temperature of the gas in the first and the second box, respectively. One of the boxes is empty into the other one. What will be the mean free path? $\lambda$ and temperature $T$ of the gas now?

$\lambda=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}, T=\frac{n_1 T_1+n_2 T_2}{n_1+n_2}$

$\lambda=\frac{n_1 \lambda_1+n_2 \lambda_2}{n_1+n_2}, T=\frac{n_1 T_1+n_2 T_2}{n_1+n_2}$

$\lambda=\frac{n_1 \lambda_1+n_2 \lambda_2}{n_1+n_2}, T=\sqrt{T_1 T_2}$

$\lambda=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}, T=\sqrt{T_1 T_2}$

IAT (IISER) 2020

MCQ (Single Correct Answer)

-1

Two identical containers kept at the same temperature carry the same gas with different molecular mean free paths $l_1$ and $l_2$. The gas from the first container is completely transferred into the second at the same temperature. What is the molecular mean free path of the resultant mixture in the second container?

$\frac{l_1 l_2}{l_1+l_2}$

$\sqrt{l_1 l_2}$

$l_1+l_2$

$\sqrt{l_1^2+l_2^2}$

IAT (IISER) 2020

MCQ (Single Correct Answer)

-1

An ideal rigid diatomic gas undergoes expansion at constant pressure when $\Delta Q$ heat is added to it. What is the ratio of the change in the internal energy $\Delta U$ to the heat supplied $\Delta Q$ ?

$\frac{\Delta U}{\Delta Q}=\frac{3}{5}$

$\frac{\Delta U}{\Delta Q}=\frac{5}{7}$

$\frac{\Delta U}{\Delta Q}=\frac{7}{9}$

$\frac{\Delta U}{\Delta Q}=\frac{2}{3}$

IAT (IISER) Subjects