In the complete combustion of butanol $C_4H_9OH_{(l)}$,if $\Delta H$ is the enthalpy of combustion and $\Delta E$ is the heat of combustion at constant volume,then

An ideal gas,$\overline{C}_{V} = \frac{5}{2} R$,is expanded adiabatically against a constant pressure of $1 \ atm$ until it doubles in volume. If the initial temperature and pressure are $298 \ K$ and $5 \ atm$,respectively,then the final temperature is . . . . . . $K$ (nearest integer). [$\overline{C}_{V}$ is the molar heat capacity at constant volume]

The $\Delta U^{\theta}$ of combustion of methane is $-X \ kJ \ mol^{-1}.$ The value of $\Delta H^{\theta}$ is

$\Delta_{vap} H^{\ominus}$ for water is $+40.49 \ kJ \ mol^{-1}$ at $1 \ bar$ and $100^{\circ} C$. The change in internal energy for this vaporization under the same conditions is . . . . . . . . . . $kJ \ mol^{-1}$. (Integer answer) (Given $R = 8.3 \ J \ K^{-1} \ mol^{-1}$)

If $65 \ kJ$ of work is done on the system and it releases $25 \ kJ$ of heat,what is the change in internal energy of the system (in $kJ$)?

For which of the following processes is $q = \Delta U$?