A certain mass of gas at 273 K is expanded to 81 times its volume under adiabatic conditions. If γ = 1 × 25 for the gas then its final temperature is

Question

A certain mass of gas at 273 K is expanded to 81 times its volume under adiabatic conditions. If &gamma; = 1 × 25 for the gas then its final temperature is (A) - 182 ° C (B) 0 ° C (C) - 235 °C (D) - 91 °C

Tardigrade Admin · Accepted Answer

Given: Initial temperature (T1)=273 K ; Initial volume (V1)=V ; Final volume (V2)=81 V and &gamma;=1.25 We know that under adiabatic condition T1 V1&gamma;-1 =T2 V2&gamma;-1 or (273/T2)=((V2/V1))1-1=((81 V/V))125-1=(81)0 ⋅ 25=3 or T2=(273/3)=91 K =-182° C (where T2 is the final temperature of the gas).

Q. A certain mass of gas at $273 K$ is expanded to $81$ times its volume under adiabatic conditions. If $γ$ = $1 \times 25$ for the gas then its final temperature is

$- 18 2^{\circ} C$

$0^{\circ} C$

$- 23 5^{\circ} C$

$- 9 1^{\circ} C$

Q. A certain mass of gas at 273K is expanded to 81 times its volume under adiabatic conditions. If γ = 1×25 for the gas then its final temperature is

−182∘C

0∘C

−235∘C

−91∘C

Q. A certain mass of gas at $273 K$ is expanded to $81$ times its volume under adiabatic conditions. If $γ$ = $1 \times 25$ for the gas then its final temperature is

$- 18 2^{\circ} C$

$0^{\circ} C$

$- 23 5^{\circ} C$

$- 9 1^{\circ} C$