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QPages 77-80: Q4: HC Verma: Concepts of Physics - Volume 2 Specific Heat Capacities of Gases Pages 77-80: Q4 Solution: The specific heat capacities of hydrogen at constant volume and …

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Mayer's relation $C_p - C_v = R/J$ strictly applies to molar heat capacities, so you must multiply the given specific heat difference by the molecular weight ($M$) to convert from cal/g to cal/mol before equating to $R/J$.

The specific heat capacities of hydrogen at constant volume and at constant pressure are 2.4 cal g−1 �C−12.4 \text{ cal g}^{-1} \text{ �C}^{-1} and 3.4 cal g−1 �C−13.4 \text{ cal g}^{-1} \text{ �C}^{-1} respectively. The molecular weight of hydrogen is 2 g mol−12 \text{ g mol}^{-1} and the gas constant, R=8.3×107 erg �C−1 mol−1R = 8.3 \times 10^7 \text{ erg �C}^{-1} \text{ mol}^{-1}. Calculate the value of J.

Step-by-Step Verified Solution

**Answer:** J=4.15×107J = 4.15 \times 10^7 erg/cal. **Step-by-Step Explanation:** Given: Cv=2.4C_v = 2.4 cal/g-�C, Cp=3.4C_p = 3.4 cal/g-�C, M=2M = 2 g/mol, R=8.3×107R = 8.3 \times 10^7 erg/mol-�C. Molar difference: (Cp−Cv)M=(3.4−2.4)×2=2(C_p - C_v)M = (3.4 - 2.4) \times 2 = 2 cal/mol-�C. Mayer's relation: Cp−Cv=R/JC_p - C_v = R/J (per mole).
2×J=8.3×107⇒J=4.15×107 erg/cal2 \times J = 8.3 \times 10^7 \Rightarrow J = 4.15 \times 10^7 \text{ erg/cal}

All Questions in this Chapter

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