$A$ monoatomic gas of $n$-moles is heated from temperature $T_1$ to $T_2$ under two different conditions: $(i)$ at constant volume and (ii) at constant pressure. The change in internal energy of the gas is

Consider the following volume-temperature $(V-T)$ diagram for the expansion of $5$ moles of an ideal monoatomic gas. Considering only $P-V$ work is involved,the total change in enthalpy (in Joule) for the transformation of state in the sequence $X \rightarrow Y \rightarrow Z$ is $\qquad$ [Use the given data: Molar heat capacity of the gas for the given temperature range,$C_{v,m} = 12 \ J \ K^{-1} \ mol^{-1}$ and gas constant,$R = 8.3 \ J \ K^{-1} \ mol^{-1}$]

When a monatomic gas expands at constant pressure,the percentages of heat supplied that is used to do external work and to increase its internal energy are respectively:

Two cylinders of equal size are filled with an equal amount of ideal diatomic gas at room temperature. Both cylinders are fitted with pistons. In cylinder $A$,the piston is free to move (isobaric process),while in cylinder $B$,the piston is fixed (isochoric process). When the same amount of heat is supplied to both cylinders,the temperature of the gas in cylinder $A$ rises by $30\, K$. What will be the rise in temperature of the gas in cylinder $B$ (in $;K$)?

An insulating cylinder contains $4 \text{ moles}$ of an ideal diatomic gas. When a heat $Q$ is supplied to it,$2 \text{ moles}$ of the gas molecules dissociate. If the temperature of the gas remains constant,then the value of $Q$ is ($R$ - universal gas constant).

Consider the thermodynamic cycle shown on the $PV$ diagram. The process $A \rightarrow B$ is isobaric,$B \rightarrow C$ is isochoric,and $C \rightarrow A$ is a straight-line process. The following internal energy change and heat are given: $\Delta U_{A \rightarrow B} = + 400 \text{ kJ}$ and $Q_{B \rightarrow C} = - 500 \text{ kJ}$. The heat flow in the process $Q_{C \rightarrow A}$ is ...... $\text{kJ}$.