Question

One mole of a monoatomic ideal gas expands adiabatically at initial temperature $T$ against a constant external pressure of $1atm$ from $1litreto3litres$. The final temperature of the gas is

• A. $T$
• B. ${\frac{T}{3}}^{\left(5R/2\right)}$
• C. $T-\frac{2}{(1.5\times 0.082)}$
• D. $T+\frac{2}{(1.5\times 0.082)}$

Answer 1

The correct option is C $T-\frac{2}{(1.5\times 0.082)}$

From the first law of thermodynamics, we have $dU=dq+dw$
For adiabatic expansion, $dq=0$.
Hence $dU=dw$ or $n{C}_V{,}_m△T$
or
$n{C}_V{,}_m△T$ = $dw$
$△T$ = $\frac{dw}{\left(n{C}_V{,}_m\right)}$

putting values, we get;

$T_f=T-\frac{P_{ext}△V}{n{C}_V,m}$

i.e.,

$T_f=T-\frac{\left(1atm\right)\left(2L\right)}{\left(1mol\right)(1.5\times 0.082Latm{K}^{-1}mo{l}^{-1})}$
$=T-\frac{2}{1.5\times 0.082}$