The molar heat capacity for an ideal gas at constant pressure is $20.785 \ J \ K^{-1} \ mol^{-1}$. The change in internal energy is $5000 \ J$ upon heating it from $300 \ K$ to $500 \ K$. The number of moles of the gas is [Nearest integer] (Given: $R = 8.314 \ J \ K^{-1} \ mol^{-1}$)

The heat of combustion of naphthalene $(C_{10}H_8(s))$ at constant volume is $-5133 \, kJ \, mol^{-1}$. The value of enthalpy change is .... $J$ $(R = 8.314 \, J \, K^{-1} \, mol^{-1}, T = 298 \, K)$.

$A$ mixture of $H_2$ and a sufficient quantity of air at $25\,^{\circ}C$ and $1\ atm$ pressure undergoes complete combustion in a closed rigid adiabatic container,leaving behind $H_2O_{(g)}$ and $N_{2(g)}$. If air is a mixture of $80\% N_2$ and $20\% O_2$ by volume and $C_{P(N_2)}$ and $C_{P(H_2O)g}$ are $7.0$ and $8.0\ cal\ deg^{-1}\ mol^{-1}$ respectively,what will be the maximum temperature attained? (Given that: $(\Delta H^o_f)_{H_2O_{(g)}} = -56.0\ kcal/mol$ and it is independent of temperature)...... $K$

For silver,$C_P \, (J \, K^{-1} \, mol^{-1}) = 23 + 0.01 \, T$. If the temperature $(T)$ of $3 \, moles$ of silver is raised from $300 \, K$ to $1000 \, K$ at $1 \, atm$ pressure,the value of $\Delta H$ will be close to $kJ$.

$A$ gas present in a cylinder expands against a constant pressure of $1 \, atm$ from a volume of $2 \, L$ to a volume of $6 \, L$. In doing so,it absorbs $800 \, J$ of heat from the surroundings. The change in internal energy of the process is ....... $J$.

$A$ sample of $n$-octane $(1.14 \ g)$ was completely burnt in excess of oxygen in a bomb calorimeter,whose heat capacity is $5 \ kJ \ K^{-1}$. As a result of the combustion reaction,the temperature of the calorimeter increased by $5 \ K$. The magnitude of the heat of combustion of octane at constant volume is $.......... \ kJ \ mol^{-1}$ (nearest integer).