Following data is known about the melting of a compound $AB$: $\Delta H = 9.2 \ kJ \ mol^{-1}$,$\Delta S = 0.008 \ kJ \ K^{-1} \ mol^{-1}$. Its melting point is:

When $3 \ mol$ of $Ar_{(g)}$ is supplied with $229 \ J$ of heat at constant pressure,the temperature of the sample increases by $2.55 \ K$. Calculate the molar heat capacity of the gas at constant volume.

$A$ thermodynamic cycle in the pressure $(p)-$ volume $(V)$ plane is given below. $A B$ and $C D$ are isothermal processes while $B C$ and $D A$ are adiabatic processes. The same cycle in the temperature $(T) -$ entropy $(S)$ plane is

Which of the following is/are true about the reversible isothermal expansion of an ideal gas?
$(a) \ \Delta U = 0$
$(b) \ q = 0$
$(c) \ \Delta T = 0$
$(d) \ q = 2.303 \ nRT \ \log_{10} \left( \frac{V_2}{V_1} \right)$

Considering the reaction $C_{(s)} + O_{2(g)} \longrightarrow CO_{2(g)} + 393.5 \ kJ$,the signs of $\Delta H, \Delta S$,and $\Delta G$ respectively are:

When $1 \ g$ of $NH_4NO_3$ is decomposed in a bomb calorimeter,the temperature of the calorimeter increases by $6.12 \ K$. If the heat capacity of the system is $1.23 \ kJ/K$,the molar enthalpy of decomposition of $NH_4NO_3$ is ........ $kJ/mol$.