Question

The molar specific heats of an ideal gas at constant pressure and volume are denoted by C_p and C_v, respectively. If `gamma = "C"_"p"/"C"_"v"` and R is the universal gas constant, then C_v is equal to ______.

विकल्प

• `"R"/((gamma - 1))`

• `((gamma - 1))/"R"`

• γR

• `(1+gamma)/(1-gamma)`

Answer 1

The molar specific heats of an ideal gas at constant pressure and volume are denoted by C_p and C_v, respectively. If `gamma = "C"_"p"/"C"_"v"` and R is the universal gas constant, then C_v is equal to `underlinebb("R"/((gamma - 1)))`.

Explanation:

C_p - C_v = R ⇒ C_p = C_v + R

∵ γ = `"C"_"p"/"C"_"v"=("C"_"v"+"R")/"C"_"v"="C"_"v"/"C"_"v"+"R"/"C"_"v"`

⇒ γ = `1+"R"/"C"_"v"`

⇒ `"R"/"C"_"v"=gamma-1`

⇒ C_v = `"R"/(gamma - 1)`