Question

Five moles of an ideal monoatomic gas at temperature T and volume 2 L expands to 8 L against a constant external pressure of 2 atm under adiabatic conditions. Then the final temperature of the gas will be:

• A. $T-\frac{8}{R}$
• B. $T-\frac{20}{3R}$
• C. $T+\frac{8}{R}$
• D. $\frac{T}{2^{\frac{5}{3}}+1}$

Answer 1

The correct option is A $T-\frac{8}{R}$

Let the final temperature be $T_2$.
For an adiabatic process, q = 0.
From the first law of thermodynamics, $△U=q+w$
$△U=w$
$△U$ = $n{C}_v\Delta T$ and $w=-P_{ext}(V_2-V_1$) for an adiabatic irreversible process.
For an monoatomic gas $C_v=\frac{3R}{2}$
$n{C}_v(T_2-T)=-P\times (V_2-V_1)$
$\frac{3}{2}\times R\times (T_2-T)=-2\times (8-2)$
$=$ $\frac{3}{2}\times R\times (T_2-T)=-12$

$T_2=$ $T-\frac{8}{R}$