Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases
An ideal gas expands from 100 cm ^3 to 200 cm ^3 at a constant pressure of 2.0 10^5 Pa when 50 J of heat is supplied to it. Assuming the initial temperature is 300 K , calculate the molar heat capacity C_V at constant volume.
Options
- A12.5 J K ⁻¹ mol ⁻¹
- B20.8 J K ⁻¹ mol ⁻¹
- C16.6 J K ⁻¹ mol ⁻¹
- D4.16 J K ⁻¹ mol ⁻¹
Correct answer
A. 12.5 J K ⁻¹ mol ⁻¹
Step-by-step solution
Work done by the gas is given by: W = P V = 2.0 10^5 (200 - 100) 10⁻⁶ = 20 J From the first law of thermodynamics: Q = U + W 50 = U + 20 U = 30 J The change in internal energy is: U = n C_V T For an isobaric process, the ideal gas equation gives P V = n R T . Thus: n T = P V R = 20 R Substituting this into the equation for U : 30 = C_V ( 20 R ) C_V = 30 R 20 = 1.5 R Using the universal gas constant R = 8.314 J K ⁻¹ mol ⁻¹ : C_V = 1.5 8.314 12.5 J K ⁻¹ mol ⁻¹