Given diagram shows an ideal gas taken from state $1$ to $2$ through optional paths, $A, B, C$ . Let $Q, W$ and $U$ represent the heat supplied to the gas, work done by the gas, and the internal energy of the gas, respectiely, then which of the following conditions is true?

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300\,K$ . the position 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   …. $K$

Which of the following is correct in terms of increasing work done for the same initial and final state

A termodynamic system is taken through the closed cycle $PQRSP$ process. The net work done by the system is …… $J$

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