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

How much energy in $kJ$ is required to convert $54 \ g$ of ice at $0 \ ^\circ C$ to water at $27 \ ^\circ C$? $\left( \Delta H_{fusion} = 6.01 \ kJ \ mol^{-1}, C_{p(liquid)} = 4.18 \ J \ K^{-1} \ g^{-1} \right)$

Consider the reaction at $300 \ K$: $H_{2(g)} + Cl_{2(g)} \to 2HCl_{(g)}$; $\Delta H^o = -185 \ kJ$. If $2 \ mole$ of $H_2$ completely react with $2 \ mole$ of $Cl_2$ to form $HCl$,what is $\Delta U^o$ for this reaction in $kJ$?

For the reaction $2X_{(s)} + 2Y_{(s)} \to 2C_{(\ell)} + D_{(g)}$,the value of $q_p$ is $-28 \, \text{kcal mol}^{-1}$ at $2700 \, ^\circ\text{C}$. Calculate the value of $q_v$ in $\text{kcal mol}^{-1}$.

$28.0 \, L$ of $CO_2$ is produced on complete combustion of $16.8 \, L$ gaseous mixture of ethene $(C_2H_4)$ and methane $(CH_4)$ at $25^{\circ}C$ and $1 \, atm$. Heat evolved during the combustion process is $......... \, kJ$.
Given :
$\Delta H_C(CH_4) = -900 \, kJ \, mol^{-1}$
$\Delta H_C(C_2H_4) = -1400 \, kJ \, mol^{-1}$

When $128 \, g$ of oxygen gas is heated from $0 \, ^oC$ to $100 \, ^oC$,the average values of $C_v$ and $C_p$ are $5 \, cal \, mol^{-1} \, K^{-1}$ and $7 \, cal \, mol^{-1} \, K^{-1}$ respectively. Find the values of $\Delta U$ and $\Delta H$.