First slide

Heat ;work and internal energy

Question

From the following data, find the magnitude of Joule's mechanical equivalent of heat. If C_p for hydrogen = 3.409 cal ${g^{- 1}}^{\circ} C^{- 1}, C_{V}$ for hydrogen = 2.409 cal $g^{- 1 \circ} C^{- 1}$ and molecular weight of hydrogen =2, then the magnitude of joule's mechanical equivalent of heat (in Jcal^-1) will be…….

Moderate

Solution

Here, J = ?
$\begin{array}{l} C_{p} = 3 .409 {calg}^{- 1 \circ} C^{- 1} \\ C_{V} = 2 .409 {calg}^{- 1 \circ} C^{- 1}, M = 2 \\ R = 8 .31 J {mol}^{- 1} K^{- 1} \\ As, C_{p} - C_{V} = \frac{r}{J} = \frac{R}{MJ} \\ ∴ 3 .409 - 2 .409 = \frac{8 .31}{2 J} \\ 1 = \frac{4 .155}{J} \\ J = 4 .16 J {cal}^{- 1} \end{array}$

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