Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases
When an ideal gas is supplied with 50 J of heat, it expands from 100 cm ^3 to 200 cm ^3 at a constant pressure of 2.0 10^5 Pa . If the initial temperature is 300 K , determine the molar heat capacity C_p at constant pressure.
Options
- A20.8 J K ⁻¹ mol ⁻¹
- B29.1 J K ⁻¹ mol ⁻¹
- C8.31 J K ⁻¹ mol ⁻¹
- D12.5 J K ⁻¹ mol ⁻¹
Correct answer
A. 20.8 J K ⁻¹ mol ⁻¹
Step-by-step solution
Given Q = 50 J , P = 2.0 10^5 Pa , V₁ = 100 cm ^3 = 10⁻⁴ m ^3 , V₂ = 200 cm ^3 = 2 10⁻⁴ m ^3 , T₁ = 300 K . From the ideal gas equation P V₁ = n R T₁ , we get: n R = P V₁ T₁ = 2.0 10^5 10⁻⁴ 300 = 20 300 = 1 15 J K ⁻¹ At constant pressure, V T , so: V₁ T₁ = V₂ T₂ 100 300 = 200 T₂ T₂ = 600 K The change in temperature is T = 600 - 300 = 300 K . The heat supplied at constant pressure is given by Q = n C_p T . Substituting the values: 50 = n C_p (300) C_p = 50 300 n = 50 300 R n R C_p = 1 6 R 1/15 = 15 6 R = 2.5 R Using