Chapter 9, Problem 9.1P

Interpretation Introduction

Interpretation:

The amount of work done should be calculated with the direction and sign of the flow of work energy.

Concept introduction:

During any reaction, work done is calculated with the help of following formula:

$W=-P\Delta V$

Where, W= work done, P= external pressure and $\Delta V=V_{final}-V_{initial}$= change in volume.

By convention, when work is done on the system the sign is positive.

When work is done by the system the sign is negative.

If energy enters into the system then the sign is positive and if the energy leaves the system then the sign is negative.

Answer to Problem 9.1P

Solution:Work done is $\text{19}\text{.166 kJ}$.

Since, the contraction of volume occurs so the sign of work done is positive and the work energy flows into the system as per convention.

Given:

Initial volume = 8.6 L

Final volume =4.3 L

External pressure= 44atm

Explanation of Solution

Here, since the volume contract so, change in volume is calculated as: $\Delta V=4.\text{3 L}-8.\text{6 L}=-4.3\text{ L}$

Work done is calculated as:

$\begin{array}{c}W=-P\Delta V\\ =-\text{44 atm}\times (-4.3L)\\ =189.2\text{ Latm}\end{array}$

Now convert L atm into kJ with the following conversion:

$\begin{array}{c}\text{1 Latm=101}\text{.3 J}\\ \text{189}\text{.2 Latm=}\frac{\text{101}\text{.3 J}}{\text{1 Latm}}\text{×189}\text{.2 Latm}\\ \text{=19165}\text{.96 J}\\ \text{=19}\text{.16596 kJ}\\ \approx \text{19}\text{.166 kJ}\end{array}$

Since, the contraction of volume occurs so the work is done on the system and sign of work done is positive. The work energy flows into the system as per convention.

Conclusion

Work done is $19.16\text{6 kJ}$. Sign of work done is positive and the work energy flows into the system as per convention.