What is the amount of work done when $0.5 \ mol$ of methane,$CH_{4(g)}$,is subjected to combustion at $300 \ K$? (Given: $R = 8.314 \ J \ K^{-1} \ mol^{-1}$)

When $x \ kJ$ heat is provided to a system,work equivalent to $y \ J$ is done on it. What is the internal energy change during this operation?

Standard enthalpy of vaporisation $\Delta_{vap}H^o$ for water at $100\ ^oC$ is $40.66\ kJ\ mol^{-1}.$ The internal energy of vaporisation of water at $100\ ^oC$ (in $kJ\ mol^{-1}$) is ............... $kJ\ mol^{-1}$ (Assume water vapour to behave like an ideal gas)

When one mole of $NH_3$ gas and one mole of $HCl$ gas are mixed in a closed container to form ammonium chloride gas,which of the following is true?

Two moles of an ideal monoatomic gas are allowed to expand adiabatically and reversibly from $300 \ K$ to $200 \ K$. The work done in the system is $... \ kJ$ $(C_V = 12.5 \ J/K/mol)$.

$A$ gas is allowed to expand in a well-insulated container against a constant external pressure of $2.5 \ atm$ from an initial volume of $2.50 \ L$ to a final volume of $4.50 \ L$. The change in internal energy $\Delta U$ of the gas in joules will be .............. $J$.