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Heat of Reaction

Two moles of ...

Question

Two moles of an ideal gas $(C_{p, m} = \frac{5}{2} R)$ is heated from 300 K to 600 K. Calculate $△ S_{g a s},$ if process is carried out at constant volume:

5 R l n 2

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\frac{3}{5} R l n 2

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3 R l n 2

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- 3 R l n 2

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Solution

The correct option is C $3 R l n 2$
We know for ideal gas, the formula to calculate change in entropy,
$△ S_{g a s} = n C_{v, m} l n \frac{T_{2}}{T_{1}} + R l n \frac{V_{2}}{V_{1}}$
At constant volume, means $V_{2} = V_{1}$
$△ S_{g a s} = n C_{v, m} l n \frac{T_{2}}{T_{1}} + R l n 1$
$△ S_{g a s} = n C_{v, m} l n \frac{T_{2}}{T_{1}}$ $∵ l n 1 = 0$
$= 2 \times (\frac{5}{2} - 1) R l n 2 ∵ (C_{v, m} = C_{p, m} - R)$
$\Rightarrow △ S_{g a s} = 3 R l n 2$

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