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Q. Heat of combustion of ethanol at constant pressure and at temperature $T K \left(= 298 K\right)$ is found to be $-q J mol^{-1}.$ Hence, heat of combustion $\left(in J\, mol^{-1}\right)$ of ethanol at the same temperature at constant volume will be:

Thermodynamics

Solution:

$C_{2}H_{5}OH\left(\ell\right)+3O_{2}\left(g\right)\to2CO_{2}\left(g\right)+3H_{2}O\left(\ell\right)$
$\Delta n_{g}=2-3=-1$
So $\Delta U=\Delta H-\Delta n_{g}RT$
$=-q+RT$