Question

One mole of an ideal monoatomic gas at temperature T and volume 3 L expands to 6 L against a constant external pressure of 2 atm under adiabatic conditions. Then the final temperature of the gas will be:

• A. $T+\frac{30}{2R}$
• B. $T-\frac{12}{3R}$
• C. $T+\frac{20}{3R}$
• D. $\frac{T}{2^{\frac{5}{3}}+1}$

Answer 1

The correct option is B $T-\frac{12}{3R}$

Let the final temperature be $T_2$.
For an adiabatic process, q = 0.
From the first law of thermodynamics, $△U=q+w$
$△U=w$
$△U$ = $n{C}_{v}dT$ and
$w=-P_{ext}(V_2-V_1$) for an adiabatic process.
For an ideal monoatomic gas $C_v=\frac{3R}{2}$
$n{C}_v(T_2-T)=-P\times (V_2-V_1)$
$\frac{3}{2}\times R\times (T_2-T)=-2\times (6-3)$
$=$ $\frac{3}{2}\times R\times (T_2-T)=-6$

$T_2=$ $T-\frac{12}{3R}$