Question

One mole of a monoatomic ideal gas expands adiabatically at initial temperature T against a constant external pressure of 1 atm from one litre to two litre. Find out the final temperature.

$[R=0.0821$ lt. atm $K^{-1}mol{e}^{-1}]$

• A. $\text{T}$
• B. $\frac{T}{5}-31$
  
• C. $T-\frac{2}{3\times 0.0821}$
• D. $T+\frac{2}{3\times 0.0821}$

Answer 1

The correct option is C $T-\frac{2}{3\times 0.0821}$

Work done against constant extemal pressure $=P_{ext}(V_2-V_1)$

In adiabatic condition $\Delta q=0$

therefore $w=\Delta u$

$-P_{ext}(V_2-V_1)=\frac{3}{2}R(T_2-T_1)$ [Expansion work is negative]

On solving, $T_2=T_1-\frac{2}{3\times 0.0821}$.

Hence, the correct option is $\text{C}$