Question

How much work is done on the gas in the process shown in Figure EX19.2?

Short answer

The amount of work done energy is 60J

Step-by-step solution

Definition of work done

The work done has represented as energy that is transferred between system and environment.

Finding the work done energy.

A the energy is transferred from gas to environment the work done is negative in the area of graph.

The area of the triangle is

$\begin{array}{rcl}& =& \frac{1}{2}∆V\times ∆p\\ & =& \frac{1}{2}\times (V_f-V_i)(∆p)\\ & =& \frac{1}{2}\times (100\times {10}^{-6}-300\times {10}^{-6})m^3(400\times {10}^3-200\times {10}^3)Pa\\ & =& -20J\\ & & \end{array}$

The area of rectangular is

$\begin{array}{rcl}& =& ∆V\times ∆p\\ & =& (V_f-V_i)(∆p)\\ & =& (100\times {10}^{-6}-300\times {10}^{-6})m^3(200\times {10}^3-0\times {10}^3)Pa\\ & =& -40J\\ & & \end{array}$

So, the total work done is the sum of triangle and rectangular $(-20J-40J)=-60J$