Question

For a certain gas, \( C_p = 29 \, {J/mol·K} \) and \( C_v = 21 \, {J/mol·K} \). What is the gas constant \( R \)?

• A. 8 J/mol·K
• B. 6 J/mol·K
• C. 10 J/mol·K
• D. 12 J/mol·K

Hint:

The difference between the specific heats at constant pressure and constant volume (\( C_p - C_v \)) gives the value of the gas constant \( R \) for an ideal gas.

Answer 1

The Correct Option is A

The relationship between the specific heat capacities at constant pressure (\( C_p \)) and constant volume (\( C_v \)) is given by the equation: \[ C_p - C_v = R \] Where \( R \) is the gas constant. Substituting the given values: \[ R = C_p - C_v = 29 \, {J/mol·K} - 21 \, {J/mol·K} = 8 \, {J/mol·K} \] Therefore, the gas constant \( R \) is \( 8 \, {J/mol·K} \).