The heat of combustion of carbon to $CO_2$ is $-393.5 \text{ kJ/mol}$. The heat released upon formation of $35.2 \text{ g}$ of $CO_2$ from carbon and oxygen gas is

For the reaction:
$CH_{4(g)} + 2O_{2(g)} \to CO_{2(g)} + 2H_2O_{(l)}$;
$\Delta_r H_{300} = -212.7 \ Kcal/mol$.
The absolute value of $\Delta_r U_{300}^o$ for this reaction is ....... $Kcal/mol$ $(R = 2 \ cal/mol-K)$.

Match the transformations in column $I$ with appropriate options in column $II$.

Column $I$	Column $II$
$A$. $CO_{2(s)} \rightarrow CO_{2(g)}$	$p$. phase transition
$B$. $CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$	$q$. allotropic change
$C$. $2H_{(g)} \rightarrow H_{2(g)}$	$r$. $\Delta H$ is positive
$D$. $P_{(\text{white, solid})} \rightarrow P_{(\text{red, solid})}$	$s$. $\Delta S$ is positive
	$t$. $\Delta S$ is negative

The work done during the combustion of $9 \times 10^{-2} \ kg$ of ethane,$C_2H_{6(g)}$ at $300 \ K$ is (Given $R = 8.314 \ J \ K^{-1} \ mol^{-1}$,atomic mass $C = 12$,$H = 1$). (in $kJ$)

Fill in the blanks given below:
$(i)$ The law of thermodynamics is actually the law of ......... .
$(ii)$ $A$ thermometer measures temperature according to the ......... law of thermodynamics.
$(iii)$ The foundation of thermochemistry is based on the ......... law of thermodynamics.
$(iv)$ The amount of heat required to raise the temperature of a substance by $1^{\circ}C$ is called the ......... of that substance.

The energy of combustion per mole of $H_2$,$LPG$,and octane follows the order: