Question

$3$ moles of hydrogen are compressed isothermally and reversibly from $60{dm}^3$ to $20{dm}^3$ and $8.22kJ$ of work is done on it. Assuming ideal behaviour, calculate the temperature of the gas.

• A. 227 K
• B. 273 K
• C. 300 K
• D. 330 K

Answer 1

Answer: (C)

300 K

Work done in isothermal, reversible process $B$ given by, $W_{max}=-2.303nRT{\log }_{10}{\left(\frac{P_2}{P_1}\right)}^{-1}$

$W_{max}=-2.303nRT{\log }_{10}\left(\frac{V_2}{V_1}\right)$

Given, Hydrogen is compossed from $60d{m}^3$ to $20d{m}^3$,

$⟹V_1=60d{m}^3,V_2=20d{m}^3$

$⟹$ no. of moles, $n=3.$

$W_{max}=8.22kJ$

$8.22KJ=-2.303\times \left(3\right)\times \left(8.314\right)\times \left(T\right)\times {\log }_{10}\left(\frac{20}{60}\right)$

$\frac{8220}{2.303\times 3\times 8.314}=T{\log }_{10}\left(\frac{60}{20}\right)$

$T=299.928K\approx 300K$

$\therefore$ Temperature of gas is $300K$.