The difference between $\Delta H$ and $\Delta U$ $(\Delta H - \Delta U),$ when the combustion of one mole of heptane $(l)$ is carried out at a temperature $T$ is equal to (in $,RT$)

For the combustion reaction $2C_8H_{18}(g) + 25O_2(g) \rightarrow 16CO_2(g) + 18H_2O(g)$,what are the signs of $\Delta H$,$\Delta S$,and $\Delta G$?

Calculate $\Delta H^{\circ}$ for the reaction, $Na_2O_{(s)} + SO_{3(g)} \longrightarrow Na_2SO_{4(s)}$, given the following reactions:
$(A) \ Na_{(s)} + H_2O_{(l)} \longrightarrow NaOH_{(s)} + \frac{1}{2}H_{2(g)} \quad \Delta H^{\circ} = -146 \ kJ$
$(B) \ Na_2SO_{4(s)} + H_2O_{(l)} \longrightarrow 2NaOH_{(s)} + SO_{3(g)} \quad \Delta H^{\circ} = +418 \ kJ$
$(C) \ 2Na_2O_{(s)} + 2H_{2(g)} \longrightarrow 4Na_{(s)} + 2H_2O_{(l)} \quad \Delta H^{\circ} = +259 \ kJ$

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

For isothermal expansion of an ideal gas, the correct combination of the thermodynamic parameters will be

$A$ 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 $J / K$)