1 mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of 27°C. The work done is 3 kJ . The final temperature of the gas is ______ K (Nearest integer). Given C = 20 J . [2023]

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Solution

Q.
1 mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of 27°C. The work done is 3 kJ ${mol}^{- 1}$ . The final temperature of the gas is ______ K (Nearest integer). Given $C_{v}$ = 20 J ${mol}^{- 1}$ $K^{- 1}$ . [2023]

Ans.
(150)

$W = - q = - n C_{V} [T_{2} - T_{1}] = 3 \times 10^{3} J$

$\Rightarrow - 1 \times 20 [T_{2} - 300] = 3 \times 1000$

$\Rightarrow - (T_{2} - 300) = \frac{3000}{20}$

$∴$ $T_{2} = 150 K$

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