4 questions from 2023
One mole of an ideal gas undergoes two different cyclic process I and II, as shown in the P–V diagrams below. In cycle I, process \( a, b, c \) and \( d \) are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, process \( a', b', c' \), and \( d' \) are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle I is \( W_I \) and that during cycle II is \( W_{II} \). The ratio \( \dfrac{W_I}{W_{II}} \) is __________. 
A closed container contains a homogeneous mixture of two moles of an ideal monatomic gas \( (\gamma = \frac{5}{3}) \) and one mole of an ideal diatomic gas \( (\gamma = \frac{7}{5}) \). Here, \( \gamma \) is the ratio of the specific heats at constant pressure and constant volume of an ideal gas. The gas mixture does a work of \( 66 \, \text{Joule} \) when heated at constant pressure. The change in its internal energy is __________ Joule.
An incompressible liquid is kept in a container having a weightless piston with a hole. A capillary tube of inner radius \( 0.1 \, \text{mm} \) is dipped vertically into the liquid through the airtight piston hole, as shown in the figure. The air in the container is isothermally compressed from its original volume \( V_0 \) to \( \frac{100}{101} V_0 \) with the movable piston. Considering air as an ideal gas, the height (\( h \)) of the liquid column in the capillary above the liquid level in \( \text{cm} \) is ____________.
[Given : Surface tension of the liquid is \( 0.075 \, \text{N m}^{-1} \), atmospheric pressure is \( 10^{5} \, \text{N m}^{-2} \) acceleration due to gravity (\( g \)) is \( 10 \, \text{m s}^{-2} \), density of the liquid is \( 10^{3} \, \text{kg m}^{-3} \) and contact angle of capillary surface with the liquid is zero] 
One mole of an ideal gas expands adiabatically from an initial state \( (T_A, V_0) \) to final state \( (T_f, 5V_0) \). Another mole of the same gas expands isothermally from a different initial state \( (T_B, V_0) \) to the same final state \( (T_f, 5V_0) \). The ratio of the specific heats at constant pressure and constant volume of this ideal gas is \( \gamma \). What is the ratio \( T_A / T_B \)?
