One mole of $CH_3OH$ is vaporized at $338 \ K$ and $1.5 \ atm$ pressure. If the enthalpy of vaporization of $CH_3OH$ is $35.57 \ kJ/mol$,calculate the value of $\Delta U$ for the process in $kJ$. (in $.76$)

Assuming the water vapour to be a perfect gas,calculate the internal energy change when $1 \ mol$ of water at $100^{\circ} C$ and $1 \ bar$ pressure is converted to ice at $0^{\circ} C$. Given the enthalpy of fusion of ice is $6.00 \ kJ \ mol^{-1}$ and heat capacity of water is $4.2 \ J \ g^{-1} {\circ} C^{-1}$.

Which among the following are true for an irreversible isothermal expansion of an ideal gas?
$(i)$ $W = -Q$
$(ii)$ $\Delta U = 0$
$(iii)$ $\Delta H \neq 0$
$(iv)$ $\Delta T = 0$

Assertion $(A)$: If heat of combustion of $C_2H_6$ is $X \ kJ \ mol^{-1}$,heat liberated on combustion of $150 \ g$ of $C_2H_6$ is $5X \ kJ$.
Reason $(R)$: Enthalpy is an extensive property.

In which of the following processes does entropy increase?

Observe the following reactions:
$AB_{(g)} + 25 H_2O_{(l)} \rightarrow AB_{(25 H_2O)} ; \Delta H = x \ kJ \ mol^{-1}$
$AB_{(g)} + 50 H_2O_{(l)} \rightarrow AB_{(50 H_2O)} ; \Delta H = y \ kJ \ mol^{-1}$
The enthalpy of dilution $(\Delta H_{dil})$ in $kJ \ mol^{-1}$ is