Discussion Forum

An ideal gas expands isothermally  and reversibly from 10m³ to 20m³ at 300 K, performing 5.187 kj of work on surrounding, calculate the number of moles of gas used

Answer:

Explanation:

$W=-\int p_{ext}.dV$

 Since the process is reversible, p_ext=p, which gives

$W=-\int p.dV$

 Substituting the ideal gas equation for p leads to

$W=-\int \frac{nRT}{V}.dV$

 since the process is isothermal,

$W=-nRTln\left(\frac{V_{2}}{V_{1}}\right)$

 $-5.187\times1000 J=-n\times8.314JK^{-1}mol^{-1}$

                                                          $ln\left(\frac{20m^{3}}{10m^{3}}\right)$

$\Rightarrow  n=\frac{5.187\times1000}{8.314\times ln2}mol$

$ =\frac{5.187\times1000}{8.314\times 0.6931}mol=3 mol$