In thermodynamics,heat and work are

An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume ($\gamma = 1.4$ and $2^{-1.4} = 0.38$). The ratio of the final to initial pressure is (in $: 1$)

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

Two cylinders $A$ and $B$ are fitted with pistons and contain equal amounts of a diatomic gas at $300 \ K$. The piston of cylinder $A$ is free to move,while the piston of cylinder $B$ is fixed. If the same amount of heat is supplied to each cylinder,the temperature of gas in $A$ increases by $30 \ K$. What is the increase in the temperature of gas in $B$ (in $K$)?

Given $P_A = 3 \times 10^4 \, Pa$,$P_B = 8 \times 10^4 \, Pa$,$V_A = 2 \times 10^{-3} \, m^3$,and $V_D = 5 \times 10^{-3} \, m^3$. An ideal gas absorbs $600 \, J$ of heat in the process $AB$ and $200 \, J$ of heat in the process $BC$. Find the change in internal energy between $A$ and $C$ in $J$.

An ideal gas undergoes a cyclic process as shown in the density-pressure graph. During the process $AB$, the work done $|W_{AB}| = 70\,J$. During the process $BC$, the gas absorbs $150\,J$ of heat. During the process $CA$, the gas undergoes expansion and does $210\,J$ of work. Which of the following statements is correct?