Chemistry - Thermodynamics - I Question with Solution | TestHub

Molar specific heat capacity at constant pressure is defined as the amount of heat energy required to raise the temperature of one mole of a substance through $1\mathrm{K}$ or $1°\mathrm{C}$ at constant pressure. It is denoted by ${\mathrm{C}}_{\mathrm{p},\mathrm{m}}$.

Molar specific heat capacity at constant volume is defined as the amount of heat energy required to raise the temperature of one mole of a substance through $1\mathrm{K}$ or $1°\mathrm{C}$ at constant volume. It is denoted by ${\mathrm{C}}_{\mathrm{v},\mathrm{m}}$.

${\mathrm{C}}_{\mathrm{v},\mathrm{m}}=\frac{1}{\mathrm{n}}\frac{∆\mathrm{U}}{∆\mathrm{T}}$

${\mathrm{C}}_{\mathrm{p},\mathrm{m}}={\mathrm{C}}_{\mathrm{v},\mathrm{m}}+\mathrm{R}$

$\Rightarrow {\mathrm{C}}_{\mathrm{v},\mathrm{m}}=20.785-8.314=12.471 {\mathrm{Jk}}^{-1}{\mathrm{ml}}^{-1}$

$\mathrm{\Delta U}={\mathrm{nC}}_{\mathrm{v},\mathrm{m}}\mathrm{\Delta T}$

$\Rightarrow \mathrm{n}=\frac{5000}{12.471\times 200}=\frac{25}{12.471}\approx 2$