Question

If 'C_p' and 'C_v' 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 'C_p' is equal to ______.

पर्याय

• `("R"gamma)/(gamma - 1)`

• γ R

• `(1 + gamma)/(1 - gamma)`

• `"R"/(gamma - 1)`

Answer 1

If 'C_p' and 'C_v' 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 'C_p' 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, C_p - C_v = R

where, R = universal gas constant

Substitute the value of C_P from the above relation in Eq. (i), we get

`gamma = "C"_"p"/("C"_"p" - "R")`

γ(C_p - R) = C_p 

⇒ γC_p - C_p = γR

C_p (γ - 1) = γR

⇒ C_p = `(gamma "R")/(gamma - 1)`

Hence, C_p is equal to `(gamma "R")/(gamma - 1)`