For hydrogen, the specific heat capacities at constant volume and at constant pressure are 2.4 cal g^ -1 ^ ^ ^ ^ -1 and 3.4 cal g^ -1 ^ ^ ^ ^ -1 respectively. The molecular weight of hydrogen is 2 g mol^ -1 and the gas

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Correct answer: A. 4.15 × 10^7 erg cal^ -1

Given specific heat capacities of hydrogen:

c_p = 3.4 \text{ cal g}^{-1} ^{}^{{}^{\circ}}\textC^{-1}

c_v = 2.4 \text{ cal g}^{-1} ^{}^{{}^{\circ}}\textC^{-1}

Molecular weight

M = 2 \text{ g mol}^{-1}

Gas constant

R = 8.3 \times 10^7 \text{ erg }^{}^{{}^{\circ}}\textC^{-1} \text{ mol}^{-1}

Molar heat capacity at constant pressure,

C_p = M c_p = 2 \times 3.4 = 6.8 \text{ cal mol}^{-1} ^{}^{{}^{\circ}}\textC^{-1}

Molar heat capacity at constant volume,

C_v = M c_v = 2 \times 2.4 = 4.8 \text{ cal mol}^{-1} ^{}^{{}^{\circ}}\textC^{-1}

According to Mayer's relation:

C_p - C_v = \dfrac{R}{J}

6.8 - 4.8 = \dfrac{8.3 \times 10^7}{J}

2.0 = \dfrac{8.3 \times 10^7}{J}

J = \dfrac{8.3 \times 10^7}{2.0} = 4.15 \times 10^7 \text{ erg cal}^{-1}

For hydrogen, the specific heat capacities at constant volume and...

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