The enthalpies of formation of gaseous $N_2O$ and $NO$ at $298 \ K$ are $82.0$ and $90.0 \ kJ \ mol^{-1}$ respectively. The enthalpy change of the reaction $N_2O_{(g)} + \frac{1}{2} O_{2(g)} \rightarrow 2 NO_{(g)}$ is

The volume of a gas decreases from $500 \ cc$ to $300 \ cc$ when a sample of gas is compressed by an average pressure of $0.6 \ atm$. During this process $10 \ J$ of heat is liberated. The change in internal energy is......$J$

In an adiabatic process,the work involved during expansion or compression of an ideal gas is given by

An ideal gas undergoes a reversible cyclic process as shown in the figure. The work done in this process is: (in $,V_1P_1$)

The molar heat capacity for an ideal gas at constant pressure is $20.785 \ J \ K^{-1} \ mol^{-1}$. The change in internal energy is $5000 \ J$ upon heating it from $300 \ K$ to $500 \ K$. The number of moles of the gas is [Nearest integer] (Given: $R = 8.314 \ J \ K^{-1} \ mol^{-1}$)

Match the following:

$(a)$ Entropy of vaporization	$(1)$ Decreases
$(b)$ $K$ for spontaneous process	$(2)$ Always has a $(+)$ value
$(c)$ Crystalline solid state	$(3)$ Has minimum entropy
$(d)$ $\Delta U$ for adiabatic expansion of an ideal gas	$(4)$ $\frac{\Delta H_{vap}}{T_b}$