In the thermodynamic processes, which of the following statements is $NOT$ true?

Two containers $A$ and $B$ contain equal volumes of an identical gas at the same pressure and temperature. The gas in container $A$ is compressed to half its original volume isothermally,while the gas in container $B$ is compressed to half its original volume adiabatically. The ratio of the final pressure of gas in container $B$ to that of gas in container $A$ is

$A$ heating element of resistance $r$ is fitted inside an adiabatic cylinder which carries a frictionless piston of mass $m$ and cross-sectional area $A$. The cylinder contains one mole of a diatomic gas. The temperature of the gas varies with time $t$ as $T = \alpha t + \frac{1}{2} \beta t^2$ (where $\alpha$ and $\beta$ are constants), while the pressure remains constant. The atmospheric pressure above the piston is $P_0$. Then:

The coefficient of isothermal elasticity $E_{\theta}$ and the coefficient of adiabatic elasticity $E_{\phi}$ are related by $(\gamma = C_p/C_v)$.

$3$ moles of an ideal monoatomic gas performs an $ABCDA$ cyclic process as shown in the figure below. The gas temperatures are $T_A=400 \, K$, $T_B=800 \, K$, $T_C=2400 \, K$, and $T_D=1200 \, K$. The work done by the gas is (approximately) $(R=8.314 \, J/mol \cdot K)$. (in $ \, kJ$)

$A$ gas follows $VT^2 = \text{constant}$. The coefficient of volume expansion of the gas is