Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases
An ideal gas sample ( = 1.5 ) is adiabatically compressed from a volume of 150 cm ^3 to 50 cm ^3 . The initial pressure and initial temperature are 150 kPa and 300 K . Calculate the molar heat capacity at constant volume for this gas. (Take R = 8.3 J K ⁻¹ mol ⁻¹ )
Options
- A12.5 J K ⁻¹ mol ⁻¹
- B8.3 J K ⁻¹ mol ⁻¹
- C16.6 J K ⁻¹ mol ⁻¹
- D24.9 J K ⁻¹ mol ⁻¹
Correct answer
C. 16.6 J K ⁻¹ mol ⁻¹
Step-by-step solution
For an ideal gas, the molar heat capacity at constant volume C_v is given by the relation: C_v = R - 1 Given that the adiabatic index = 1.5 and the universal gas constant R = 8.3 J K ⁻¹ mol ⁻¹ , substituting these values yields: C_v = 8.3 1.5 - 1 C_v = 8.3 0.5 = 16.6 J K ⁻¹ mol ⁻¹ The values of initial volume, final volume, pressure, and temperature are extraneous for this calculation.