Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q: \Delta U: \Delta W$ is
[Given $\rightarrow \Delta Q=$ heat supplied,$\Delta U=$ change in internal energy,$\Delta W$ $=$ work done]

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

$A$ soap bubble of radius $r$ contains a monoatomic ideal gas. The gas is heated in such a manner that the bubble remains in mechanical equilibrium. Assuming that the soap material of the bubble has no heat capacity,the molar heat capacity of the gas in the process will be (Neglect atmospheric pressure). (in $R$)

$A$ monoatomic gas of pressure $P$ having volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is (ratio of specific heats $\gamma = \frac{5}{3}$)

Two cylinders $A$ and $B$ fitted with pistons contain equal amount of an ideal diatomic gas at $303 \text{ K}$. The piston of cylinder $A$ is free to move and that of cylinder $B$ 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 cylinder $B$ is $63 \text{ K}$, then the rise in temperature of the gas in $A$ is: (in $\text{ K}$)

Answer the following questions based on the $P-T$ phase diagram of $CO_{2}$:
$(a)$ $CO_{2}$ at $1 \; atm$ pressure and temperature $-60^{\circ} C$ is compressed isothermally. Does it go through a liquid phase?
$(b)$ What happens when $CO_{2}$ at $4 \; atm$ pressure is cooled from room temperature at constant pressure?
$(c)$ Describe qualitatively the changes in a given mass of solid $CO_{2}$ at $10 \; atm$ pressure and temperature $-65^{\circ} C$ as it is heated up to room temperature at constant pressure.
$(d)$ $CO_{2}$ is heated to a temperature $70^{\circ} C$ and compressed isothermally. What changes in its properties do you expect to observe?