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Question
The specific heat capacities of hydrogen at constant volume and at constant pressure are 2.4 cal g−1 °C−1 and 3.4 cal g−1 °C−1 respectively. The molecular weight of hydrogen is 2 g mol−1 and the gas constant, R = 8.3 × 107 erg °C−1 mol−1. Calculate the value of J.
Solution
Specific heat capacity at constant volume, Cv(H2) = 2.4 cal/g-°C
Specific heat capacity at constant pressure, Cp(H2) = 3.4 cal/g-°C
Molecular weight, M = 2 g/mol
Gas constant, R = 8.3 × 107 erg/mol-°C
We know: Cp − Cv = 1 cal/g-°C,
where Cp and Cv are molar specific heat capacities.
So, difference of molar specific heat,
Cp × M − Cv × M = 1 cal/mol-°C
Now, 2 × J = R
⇒ 2 × J = 8.3 × 107 erg/mol-°C
⇒ J = 4.15 × 107 erg/cal
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