1)

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


A) 1.5

B) 1

C) 3

D) 2

Answer:

Option C

Explanation:

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

 Since the process is reversible, pext=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$