MCQ
A certain mass of gas at $273 K$ is expanded to $81$ times its volume under adiabatic condition. If $\gamma = 1.25$ for the gas, then its final temperature is ..... $^oC$
- A$-235$
- ✓$-182$
- C$-91$
- D$0$
✓
Answer
Correct option: B.
$-182$
b
(b) For adiabatic process $T{V^{\gamma - 1}}$= constant
(b) For adiabatic process $T{V^{\gamma - 1}}$= constant
==> $\frac{{{T_2}}}{{{T_1}}} = {\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^{\gamma - 1}}$==> ${T_2} = {\left( {\frac{{{V_1}}}{{{V_2}}}} \right)^{\gamma - 1}} \times {T_1}$
==> ${T_2} = {\left( {\frac{1}{{81}}} \right)^{1.25 - 1}} \times 273$$ = {\left( {\frac{1}{{81}}} \right)^{0.25}} \times 273$
$ = \frac{{273}}{3} = 91K = \,-182°C$
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