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	$(4)$ $\frac{\Delta H_{vap}}{T_b}$

$5 \, mol$ of an ideal gas at $100 \, K$ are allowed to undergo reversible compression till its temperature becomes $200 \, K$. If $C_v = 28 \, J \, K^{-1} \, mol^{-1}$,calculate $\Delta U$ and $\Delta pV$ for this process. $(R = 8.0 \, J \, K^{-1} \, mol^{-1})$

$200 \ mL$ of $0.2 \ M \ HCl$ is mixed with $300 \ mL$ of $0.1 \ M \ NaOH$. The molar heat of neutralization of this reaction is $-57.1 \ kJ \ mol^{-1}$. The increase in temperature in $^{\circ}C$ of the system on mixing is $x \times 10^{-2}$. The value of $x$ is ....... . (Nearest integer)
[Given : Specific heat of water $= 4.18 \ J \ g^{-1} \ K^{-1}$
Density of water $= 1.00 \ g \ cm^{-3}$]
(Assume no volume change on mixing)

The enthalpy of vaporization of a liquid at $500 \, K$ and $1 \, atm$ pressure is $10 \, kcal \, mol^{-1}$. The change in internal energy $(\Delta U)$ for $3 \, moles$ of the liquid at the same temperature and pressure is ............ $kcal$.

$A$ mixture of $H_2$ and a sufficient quantity of air at $25\,^{\circ}C$ and $1\ atm$ pressure undergoes complete combustion in a closed rigid adiabatic container,leaving behind $H_2O_{(g)}$ and $N_{2(g)}$. If air is a mixture of $80\% N_2$ and $20\% O_2$ by volume and $C_{P(N_2)}$ and $C_{P(H_2O)g}$ are $7.0$ and $8.0\ cal\ deg^{-1}\ mol^{-1}$ respectively,what will be the maximum temperature attained? (Given that: $(\Delta H^o_f)_{H_2O_{(g)}} = -56.0\ kcal/mol$ and it is independent of temperature)...... $K$

$1 \, \text{mole}$ of $H_2SO_4$ is mixed with $2 \, \text{moles}$ of $NaOH$. The heat evolved will be