For the reaction,$C_3H_{8(g)} + 5O_{2(g)} \to 3CO_{2(g)} + 4H_2O_{(l)}$ at constant temperature,$\Delta H - \Delta E$ is

Two moles of an ideal gas are allowed to expand from a volume of $10 \ dm^3$ to $2 \ m^3$ at $300 \ K$ against a pressure of $101.325 \ kPa$. Calculate the work done. (in $kJ$)

Which of the following is the correct mathematical expression for the first law of thermodynamics?

At the $1$ bar pressure,the volume of a gas is $0.6 \ L$. If the gas receives $122 \ J$ of heat at $1$ bar pressure,the volume becomes $2 \ L$. Calculate the change in its internal energy. $(1 \ L \cdot bar = 101.32 \ J)$

Observe the following reaction: $ABO_{3(s)} \xrightarrow{1000 \ K} AO_{(s)} + BO_{2(g)}$. $\Delta_{r} H$ for this reaction is $x \ kJ \ mol^{-1}$. What is its $\Delta_{r} U$ (in $kJ \ mol^{-1}$) at the same temperature? $(R = 8.3 \ J \ mol^{-1} \ K^{-1})$

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)