A given ideal gas with γ = C v C p = 1.5 at a temperature T . If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

Question

A given ideal gas with γ = C v ​ C p ​ ​ = 1.5 at a temperature T . If the gas is compressed adiabatically to one-fourth of its initial volume, the final temperature will be

TestHub · Accepted Answer

T V γ − 1 = constant ​ T 1 ​ V 1 γ − 1 ​ = T 2 ​ V 2 γ − 1 ​ ⇒ T ( V ) 1/2 = T 2 ​ ( 4 V ​ ) 1/2 [ ∵ γ = 1.5 , T 1 ​ = T , V 1 ​ = V and V 2 ​ = 4 V ​ ] ∴ T 2 ​ = ( V 4 V ​ ) 1/2 T = 2 T ​

Physics - Heat & Thermo Question with Solution | TestHub

Options:

Doubts & Discussion