Chapter 14, Problem 14.1P

Interpretation Introduction

Interpretation:

Work done by system when volume expands from $10\text{ L}$ to $25\text{ L}$ has to be determined.

Concept Introduction:

Thermodynamics is a study of energy transfers that can be done by either heat or work. The energy transferred through work involves force. When work is positive then system gains energy while when work is negative then system loses energy. The expression to calculate work is as follows:

  $w=-P\left(V_{\text{f}}-V_{\text{i}}\right)$        (1)

Here $P$ is pressure, $V_{\text{f}}$ is the final volume, and $V_{\text{i}}$ is initial volume.

Answer to Problem 14.1P

The work done by system is $-5319.6\text{ J}$.

Explanation of Solution

Substitute $3.5\text{ atm}$ for $P$, $10\text{ L}$ for $V_{\text{i}}$, and $25\text{ L}$ for $V_{\text{f}}$ in equation (1).

  $\begin{array}{c}w=-\left(3.5\text{ atm}\right)\left(25\text{ L}-10\text{ L}\right)\\ =-\left(52.5\text{ L}\cdot \text{atm}\right)\left(\frac{101.325\text{ J}}{1\text{ L}\cdot \text{atm}}\right)\\ =-5319.6\text{ J}\end{array}$