Which of the following equations are correct?
$(A)$ $H = U + PV$
$(B)$ $G = H - TS$
$(C)$ $U = q + W$

For silver,$C_P \, (J \, K^{-1} \, mol^{-1}) = 23 + 0.01 \, T$. If the temperature $(T)$ of $3 \, moles$ of silver is raised from $300 \, K$ to $1000 \, K$ at $1 \, atm$ pressure,the value of $\Delta H$ will be close to $kJ$.

$A$ calorimeter contains $0.2 \ kg$ of water at $30^{\circ} C$. $0.1 \ kg$ of water at $60^{\circ} C$ is added to it,the mixture is well stirred and the resulting temperature is found to be $35^{\circ} C$. The water equivalent of the calorimeter is $:-$ (in $J / K$)

The internal energy change (in $J$) when $90 \ g$ of water undergoes complete evaporation at $100^{\circ} C$ is........
(Given: $\Delta H_{vap}$ for water at $373 \ K = 41 \ kJ/mol$,$R = 8.314 \ J \ K^{-1} mol^{-1}$)

For the reaction
$A_{(\ell)} \rightarrow 2 B_{(g)}$
$\Delta U = 2.1 \; kcal, \Delta S = 20 \; cal \; K^{-1} \; mol^{-1}$ at $300 \; K$
Hence $\Delta G$ in $kcal \; mol^{-1}$ is

One gram sample of $NH_4NO_3$ is decomposed in a bomb calorimeter. The temperature of the calorimeter increases by $6.12 \ K$. The heat capacity of the system is $1.23 \ kJ/K$. What is the molar heat of decomposition for $NH_4NO_3$ in $kJ/mol$?