Question

Calculate the work done by the system in an irreversible (single step) adiabatic expansion of 2 mole of a polyatomic gas $(\gamma -\frac{4}{3})$ from 300K and pressure 10 atm to 1 atm:

• A. - 227 R
• B. - 890 Cal mole^-1 K^-1
• C. - 405 R
• D. - 53.67 kJ mole^-1 K^-1

Answer 1

The correct option is D

- 53.67 kJ mole^-1 K^-1

$2\times C_{V_{1}M}(T_2-T_1)=[\frac{2R{T}_2}{1}-\frac{2R{T}_1}{10}]$

$\gamma =\frac{4}{3}=\frac{C_{P_{1}M}}{C_{V_{1}M}}$ and $C_{P_{1}M}=C_{V_{1}M}+R$

$\therefore C_{V_{1}M}=3R$

$3R(T_2-300)=-R{T}_2+\frac{R\times 300}{10}$

$T_2=232.5K$

$W=\Delta U=2\times 3R(300-232.5)$

$W=-405R$