Question

a. The molar heat capacities of a gas at constant pressure
and constant volume are 28.8 J mol−1
K−1
and 20.5 J mol−1
K−1
respectively.
Calculate the gas constant.

Answer 1

Answer on Question #75088, Physics / Molecular Physics | Thermodynamics

The molar heat capacities of a gas at constant pressure and constant volume are $28.8\ \mathrm{J\ mol^{-1}\ K^{-1}}$ and $20.5\ \mathrm{J\ mol^{-1}\ K^{-1}}$ respectively. Calculate the gas constant.

Answer:

In the adiabatic process, the adiabatic exponent is

$$\gamma = 1 + \frac{R}{c_V}$$

We know the adiabatic index

$$\gamma = \frac{c_p}{c_V}$$

We compare these two equations

$$\frac{c_p}{c_V} = 1 + \frac{R}{c_V}$$

We get

$$R = c_p - c_V$$ $$R = 28.8\ \mathrm{J\ mol^{-1}\ K^{-1}} - 20.5\ \mathrm{J\ mol^{-1}\ K^{-1}} = 8.3\ \mathrm{J\ mol^{-1}\ K^{-1}}$$

Answer: $8.3\ \mathrm{J\ mol^{-1}\ K^{-1}}$

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