Question

An ideal monoatomic gas at 300K expands adiabatically to twice its volume. What is the final temperature?

Answer 1

The final temperature of the given monoatomic gas is 188.55 K.

- It is given that :

Initial temp T₁ = 300 K

Final temp T₂ = ?

Initial volume V₁ = V

Final volume V₂ = 2 V

γ = 5/3 ( For monoatomic gas)

- For an adiabatic process,

TV^(γ-1) = constant

⇒T₁V₁^(γ-1) = T₂V₂^(γ-1)

⇒(T₂/T₁) = (V₁/V₂)^(γ-1)

(T₂/300) = (V/2V)^(5/3-1)

(T₂/300) = (1/2)^2/3

T₂ = 0.6285 × 300

T₂ = 188.55 K