First slide

Heat given

Question

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

Easy

A

108.7 J
B

29 J
C

215.3 J
D

124 J

Solution

$\begin{array}{l} C_{p} = \frac{5}{2} \cdot R and C_{V} = \frac{3}{2} \cdot R \\ ∴ \frac{Q_{V}}{Q_{p}} = \frac{3}{5} or \frac{Q_{V}}{207 J} = \frac{3}{5} \\ or Q_{V} = \frac{207 \times 3}{5} = 124 J \end{array}$

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