Question:
The difference between two molar specific heats of a gas is \(7000\) J-kg\({}^{-1}\)-K\({}^{-1}\). If the ratio of two specific heats of gas is \(7/5\), the molar specific heat of the gas at constant pressure in J-kg\({}^{-1}\)-K\({}^{-1}\) is
The difference between two molar specific heats of a gas is \(7000\) J-kg\({}^{-1}\)-K\({}^{-1}\). If the ratio of two specific heats of gas is \(7/5\), the molar specific heat of the gas at constant pressure in J-kg\({}^{-1}\)-K\({}^{-1}\) is
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Use Cp minus Cv equal to the given difference together with the ratio Cp over Cv equal to 7/5.
Updated On: Nov 12, 2026
- \(17500\)
- \(18500\)
- \(24500\)
- \(25500\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
Given \(C_p-C_v=7000\) and \(\gamma=\dfrac{C_p}{C_v}=\dfrac{7}{5}\).
Step 2: Express in one variable
\(C_p=\dfrac{7}{5}C_v\)
\(\dfrac{7}{5}C_v-C_v=7000\)
\(\dfrac{2}{5}C_v=7000\)
Step 3: Calculation
\(C_v=17500\)
\(C_p=\dfrac{7}{5}\times17500=24500\) J-kg\(^{-1}\)-K\(^{-1}\)
Final Answer:
The specific heat at constant pressure is 24500. \[ \boxed{\text{(C) }24500} \]
Given \(C_p-C_v=7000\) and \(\gamma=\dfrac{C_p}{C_v}=\dfrac{7}{5}\).
Step 2: Express in one variable
\(C_p=\dfrac{7}{5}C_v\)
\(\dfrac{7}{5}C_v-C_v=7000\)
\(\dfrac{2}{5}C_v=7000\)
Step 3: Calculation
\(C_v=17500\)
\(C_p=\dfrac{7}{5}\times17500=24500\) J-kg\(^{-1}\)-K\(^{-1}\)
Final Answer:
The specific heat at constant pressure is 24500. \[ \boxed{\text{(C) }24500} \]
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