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Question
If 'Cp' and 'Cv' are molar specific heats of an ideal gas at constant pressure and volume respectively. If 'λ' is the ratio of two specific heats and 'R' is universal gas constant then 'Cp' is equal to ______.
Options
`("R"gamma)/(gamma - 1)`
γ R
`(1 + gamma)/(1 - gamma)`
`"R"/(gamma - 1)`
Solution
If 'Cp' and 'Cv' are molar specific heats of an ideal gas at constant pressure and volume respectively. If 'λ' is the ratio of two specific heats and 'R' is universal gas constant then 'Cp' is equal to `underline(("R"gamma)/(gamma - 1))`.
Explanation:
Given, that `"C"_"p"/"C"_"v" = gamma` ...(i)
As we know that from Mayer's relation, Cp - Cv = R
where, R = universal gas constant
Substitute the value of CP from the above relation in Eq. (i), we get
`gamma = "C"_"p"/("C"_"p" - "R")`
γ(Cp - R) = Cp
⇒ γCp - Cp = γR
Cp (γ - 1) = γR
⇒ Cp = `(gamma "R")/(gamma - 1)`
Hence, Cp is equal to `(gamma "R")/(gamma - 1)`
