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Question
The molar specific heat of an ideal gas at constant pressure and constant volume is 'Cp' and 'Cv' respectively. If 'R' is the universal gas constant and the ratio 'Cp' to 'Cv' is 'γ' then CV = ______.
Options
`(1-gamma)/(1+gamma)`
`(1+gamma)/(1-gamma)`
`(gamma-1)/"R"`
`"R"/(gamma-1)`
MCQ
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Solution
The molar specific heat of an ideal gas at constant pressure and constant volume is 'Cp' and 'Cv' respectively. If 'R' is the universal gas constant and the ratio 'Cp' to 'Cv' is 'γ' then CV = `underline("R"/(gamma-1))`
Explanation:
Given:
`"C"_"p"/"C"_"v"= gamma`
`therefore ("C"_"p" - "C"_"v")/"C"_"v"= (gamma - 1)/1`
`therefore "R"/"C"_"v"= gamma - 1` ....`(because "C"_"p" - "C"_"v" = "R")`
`therefore "C"_"v" = "R"/ (gamma - 1)`
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