One mole of an ideal gas requires 207 J heat to raise the temperature by 10 K when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same 10 K, the heat required is: (Given gas constant $R = 8.3 J {mol}^{- 1} K)$

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198.7 J

29 J

215.3 J

124 J

answer is D.

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Detailed Solution

$(Δ Q)_{P} = μ C_{p} Δ T \Rightarrow 207 = 1 \times C_{p} \times 10$

$\begin{array}{l} \Rightarrow C_{P} = 20 .7 \frac{Joule}{mol - K} . Also \\ C_{P} - C_{V} = R \\ \Rightarrow C_{V} = C_{P} - R = 20 .7 - 8 .3 = 12.4 J / mole / k \end{array}$

$\begin{array}{l} S o, (Δ Q)_{V} = μ C_{V} Δ T = 1 \times 12.4 \times 10 \\ = 124 J \end{array}$

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