The isothermal Bulk modulus of an ideal gas at pressure $P$ is

A monoatomic ideal gas, initially at temperature $T_1$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively, then $T_1/T_2$ is given by

Calculate heat given to gas during process $ABA$ in figure …… $J$

Two cylinders $A $ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300\ K.$ The piston of $A$ is free to move while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30\ K,$ then the rise in temperature of the gas in $B$ is  ……. $K$

One mole of an ideal gas $\left( {\frac{{{C_p}}}{{{C_v}}} = Y} \right)$ heated by law $P = \alpha V$ where $P$ is pressure of gas, $V$ is volume, $\alpha $ is a constant. What is the molar heat capacity of gas in the process