Chapter U5.107, Problem 3E

Interpretation Introduction

Interpretation: The work done by the gas if the volume of the gases increases from 0.5 L to 12.5 L against the pressure of 1.2 atm needs to be determined.

Concept Introduction: The gaseous state of matter contains particles with the largest intermolecular distance and the least intermolecular force of attraction.

Because of high kinetic energy between particles, gases can easily expand and the work done by the gaseous system during expansion can be calculated with the help of following equation:

  $\begin{array}{l}\text{w = }{\displaystyle {\int }_{\text{v1}}^{\text{v2}}\text{pdv}}\\ {\text{w = p (V}}_{\text{2}}\text{ - V}\text{)}\end{array}$

Answer to Problem 3E

W = 1.46 kJ

Explanation of Solution

Given information:

V₂ = 12.5 L

V₁ = 0.5 L

P =1.2 atm

  $\begin{array}{l}\text{w = }{\displaystyle {\int }_{{\text{v}}_{\text{1}}}^{{\text{v}}_{\text{2}}}\text{PdV}}\\ {\text{w =P (V}}_{\text{2}}\text{ - V}\text{)}\end{array}$

Substitute the values to calculate w:

  $\begin{array}{l}\text{w = }{\displaystyle {\int }_{{\text{v}}_{\text{1}}}^{{\text{v}}_{\text{2}}}\text{PdV}}\\ {\text{w = P(V}}_{\text{2}}\text{ - V}\text{)}\\ \text{w = 1}\text{.2 atm (12}\text{.5- 0}\text{.5)L}\\ \text{w = 14}\text{.4 atm}\text{.L}\end{array}$

Convert work from L.atm to J:

1 L.atm= 101.325 J

  $\text{14}\text{.4 atm}\text{.L×}\frac{\text{101}\text{.325J}}{\text{1 L}\text{.atm}}\text{×}\frac{\text{1kJ}}{\text{1000J}}\text{= 1}\text{.46 kJ}$

Conclusion

Thus,

W = 1.46 kJ