The slopes of the isothermal and adiabatic $p-V$ graphs of a gas are $S_I$ and $S_A$ respectively. If the heat capacity ratio of the gas is $\frac{3}{2}$,then $\frac{S_I}{S_A}=$

An ideal gas goes through a reversible cycle $a \to b \to c \to d$ and has the $V - T$ diagram shown below. Processes $d \to a$ and $b \to c$ are adiabatic. The corresponding $P - V$ diagram for the process is (all figures are schematic and not drawn to scale):

Two identical adiabatic vessels are filled with oxygen at pressure $P_1$ and $P_2$ $(P_1 > P_2)$. The vessels are interconnected with each other by a non-conducting pipe. If $U_{01}$ and $U_{02}$ denote the initial internal energy of oxygen in the first and second vessel respectively,and $U_{f1}$ and $U_{f2}$ denote the final internal energy values,then:

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 $K$)?

$A$ cyclic process $ABCD$ is shown in the $P-V$ diagram. Which of the following curves represent the same process?

Helium gas undergoes a cycle $ABCDA$ (consisting of two isochoric and two isobaric lines) as shown in the figure. The efficiency of this cycle is nearly ....... $\%$ (Assume the gas to be an ideal gas).