A diatomic gas initially at 18°C is compressed adiabatically to one eighth of its original volume. The temperature after compression will be

(a) 18° C

(b) 668.4° K

(c) 395.4° C

(d) 144° C

(b)

Initial temperature (T₁) = 18°C = 291 K

Let Initial volume (V₁) = V

Final volume (V₂) =  

According to adiabatic process,

TV^g-1 = constant

According to question, T₁ V₁^y-1 = T₂ V₂^y-1

Dear Student,
Please find below the solution to your problem.

T1 ​= 18oC = (273+18) = 291K
and V2​ = V1​/8
We know that TV^(γ−1) = constant
or, T2​V2^(γ−1) ​= T1​V1^(γ−1​)
T2 ​= T1​(V2/​V1​​)^(γ−1)
= 291 × (8)^(1.4−1)
= 668.5K
= 395.5oC

Thanks and Regards