A certain ideal gas has the following properties: Molecular Mass, M = 24.943416 kg/kmole and Cvo = 1.000 kJ/ºK/kg. Determine Cpo in kJ / °K / kg.

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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**Problem Statement:**

A certain ideal gas has the following properties:

- Molecular Mass, \( M = 24.943416 \, \text{kg} / \text{kmole} \)
- \( C_{V_0} = 1.000 \, \text{kJ} / \left( \text{K} \cdot \text{kg} \right) \)

Determine \( C_{p_0} \) in \( \text{kJ} / \left( \text{K} \cdot \text{kg} \right) \).

**Explanation:**

This problem asks us to determine the specific heat capacity at constant pressure (\( C_{p_0} \)) for a given ideal gas based on its molecular mass and specific heat capacity at constant volume (\( C_{V_0} \)). The given molecular mass is \( 24.943416 \, \text{kg} / \text{kmole} \), and the given specific heat capacity at constant volume is \( 1.000 \, \text{kJ} / \left( \text{K} \cdot \text{kg} \right) \).

To solve this problem, we can use the following relation for an ideal gas:

\[ C_p = C_V + R \]

Where:
- \( R \) is the specific gas constant.

The specific gas constant \( R \) for a gas is given by the universal gas constant \( \hat{R} \) divided by the molar mass \( M \) of the gas:

\[ R = \frac{\hat{R}}{M} \]

Given:
- Universal gas constant, \( \hat{R} = 8.314 \, \text{kJ} / \left( \text{K} \cdot \text{kmole} \right) \)
- Molecular mass, \( M = 24.943416 \, \text{kg} / \text{kmole} \)
- \( C_{V_0} = 1.000 \, \text{kJ} / \left( \text{K} \cdot \text{kg} \right) \)

Using these values, we can determine the specific gas constant \( R \):

\[ R = \frac{8.314 \, \text{kJ} / \left( \text{K}
Transcribed Image Text:**Problem Statement:** A certain ideal gas has the following properties: - Molecular Mass, \( M = 24.943416 \, \text{kg} / \text{kmole} \) - \( C_{V_0} = 1.000 \, \text{kJ} / \left( \text{K} \cdot \text{kg} \right) \) Determine \( C_{p_0} \) in \( \text{kJ} / \left( \text{K} \cdot \text{kg} \right) \). **Explanation:** This problem asks us to determine the specific heat capacity at constant pressure (\( C_{p_0} \)) for a given ideal gas based on its molecular mass and specific heat capacity at constant volume (\( C_{V_0} \)). The given molecular mass is \( 24.943416 \, \text{kg} / \text{kmole} \), and the given specific heat capacity at constant volume is \( 1.000 \, \text{kJ} / \left( \text{K} \cdot \text{kg} \right) \). To solve this problem, we can use the following relation for an ideal gas: \[ C_p = C_V + R \] Where: - \( R \) is the specific gas constant. The specific gas constant \( R \) for a gas is given by the universal gas constant \( \hat{R} \) divided by the molar mass \( M \) of the gas: \[ R = \frac{\hat{R}}{M} \] Given: - Universal gas constant, \( \hat{R} = 8.314 \, \text{kJ} / \left( \text{K} \cdot \text{kmole} \right) \) - Molecular mass, \( M = 24.943416 \, \text{kg} / \text{kmole} \) - \( C_{V_0} = 1.000 \, \text{kJ} / \left( \text{K} \cdot \text{kg} \right) \) Using these values, we can determine the specific gas constant \( R \): \[ R = \frac{8.314 \, \text{kJ} / \left( \text{K}
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