The specific heat of a monoatomic gas at constant pressure is 248.2 J kg-1 K-1 and at constant volume it is 149.0 J kg-1 K-1. Find the mean molar mass of the gas.

Question

The specific heat of a monoatomic gas at constant pressure is 248.2 J kg-1 K-1 and at constant volume it is 149.0 J kg-1 K-1. Find the mean molar mass of the gas. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Molar heat capacity at constant pressure,

C_{p} = 248.2 \times M J k g^{- 1}

where

M

is the molar mass of the gas.
Similarly,

C_{v} = 149 \times M J k g^{- 1}

C_{P} - C_{v} = R

∴ 248.2 \times M - 149 M = 8.314

M = \frac{8.314}{248.2 - 149} = 0.0838 k g /

mol
Molar mass of the gas

= 83.8 g

/mol

Q. The specific heat of a monoatomic gas at constant pressure is 248.2Jkg−1K−1 and at constant volume it is 149.0Jkg−1K−1. Find the mean molar mass of the gas.

Molar heat capacity at constant pressure, Cp​=248.2×MJkg−1 where M is the molar mass of the gas. Similarly, Cv​=149×MJkg−1 CP​−Cv​=R ∴248.2×M−149M=8.314 M=248.2−1498.314​=0.0838kg/mol Molar mass of the gas =83.8g/mol

Q. The specific heat of a monoatomic gas at constant pressure is $248.2 J k g^{- 1} K^{- 1}$ and at constant volume it is $149.0 J k g^{- 1} K^{- 1}$ . Find the mean molar mass of the gas.