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Prove (°C ), - r(WP) and (°CF ), --r(3) - T ӘР For ideal gas, pV=RT. Show that Cy is independent of the volume and Cp is independent of the pressure.

Prove (°C ), - r(WP) and (°CF ), --r(3) - T ӘР For ideal gas, pV=RT. Show that Cy is independent of the volume and Cp is independent of the pressure.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Exercise 2:** Prove the following equations: \[ \left( \frac{\partial C_V}{\partial V} \right)_T = T \left( \frac{\partial^2 P}{\partial T^2} \right)_V \] and \[ \left( \frac{\partial C_P}{\partial P} \right)_T = -T \left( \frac{\partial^2 V}{\partial T^2} \right)_P \] For an ideal gas, the equation \( pV = RT \) holds. Demonstrate that \( C_V \) is independent of the volume, and \( C_P \) is independent of the pressure.
Transcribed Image Text:**Exercise 2:** Prove the following equations: \[ \left( \frac{\partial C_V}{\partial V} \right)_T = T \left( \frac{\partial^2 P}{\partial T^2} \right)_V \] and \[ \left( \frac{\partial C_P}{\partial P} \right)_T = -T \left( \frac{\partial^2 V}{\partial T^2} \right)_P \] For an ideal gas, the equation \( pV = RT \) holds. Demonstrate that \( C_V \) is independent of the volume, and \( C_P \) is independent of the pressure.
Expert Solution
Step 1

Part A:

It is required to prove ∂CV∂VT = T∂2p∂T2V.

Part B:

It is required to prove ∂Cp∂pT = -T∂2V∂T2p.

Part C:

It is required to show that CV is independent of volume and Cp is independent of pressure.

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