Question:
For a gas, \( C_p - C_v = R \). If \( C_v = 2R \), then \( C_p \) is:
For a gas, \( C_p - C_v = R \). If \( C_v = 2R \), then \( C_p \) is:
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Specific heat at constant pressure (\( C_p \)) is always greater than specific heat at constant volume (\( C_v \)) because at constant pressure, heat is used not only to increase internal energy but also to do work during expansion.
Updated On: Jun 3, 2026
- \( R \)
- \( 2R \)
- \( 3R \)
- \( 4R \)
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The Correct Option is C
Solution and Explanation
Concept:
The relationship between the molar specific heat capacity at constant pressure (\( C_p \)) and the molar specific heat capacity at constant volume (\( C_v \)) for an ideal gas is known asMayer's Relation**.
• Formula: \( C_p - C_v = R \)
• \( C_p \): Molar specific heat at constant pressure.
• \( C_v \): Molar specific heat at constant volume.
• \( R \): Universal gas constant.
Step 1: Identifying the given information.
Relationship: \( C_p - C_v = R \)
Given value: \( C_v = 2R \)
Step 2: Substituting the value of \( C_v \) into Mayer's Relation.
\[ C_p - (2R) = R \]
Step 3: Solving for \( C_p \).
To find \( C_p \), move \( 2R \) to the right side of the equation: \[ C_p = R + 2R \] \[ C_p = 3R \]
• Formula: \( C_p - C_v = R \)
• \( C_p \): Molar specific heat at constant pressure.
• \( C_v \): Molar specific heat at constant volume.
• \( R \): Universal gas constant.
Step 1: Identifying the given information.
Relationship: \( C_p - C_v = R \)
Given value: \( C_v = 2R \)
Step 2: Substituting the value of \( C_v \) into Mayer's Relation.
\[ C_p - (2R) = R \]
Step 3: Solving for \( C_p \).
To find \( C_p \), move \( 2R \) to the right side of the equation: \[ C_p = R + 2R \] \[ C_p = 3R \]
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