Question

80 J of work are done on the gas in the process shown in Figure EX19.3. What is V1 in cm3 ?

Short answer

The value of $V_I$is$200c{m}^3$

Step-by-step solution

Definition of work done

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

Step  2: Finding the volume through work done energy.

As it is isothermal process , work done is positive.

The area of the triangle is

$\begin{array}{rcl}& =& \frac{1}{2}∆V\times ∆p\\ & =& \frac{1}{2}\times (3V_1-V_1)(∆p)\\ & =& \frac{1}{2}\times \left(2V_1\right)(300\times {10}^3-100\times {10}^3)Pa\\ & =& (100\times {10}^3)Pa\\ & & \end{array}$

The area of rectangular is

$\begin{array}{rcl}& =& ∆V\times ∆p\\ & =& (V_1-V_1)(∆p)\\ & =& \left(2V_1\right)(100\times {10}^3-0\times {10}^3)V_{1}Pa\\ & =& \left(2V_1\right)(100\times {10}^3)Pa\\ & & \end{array}$

So the total work done is

$\begin{array}{rcl}& =& \left(2V_1\right)(100\times {10}^3)Pa+\left(2V_1\right)(100\times {10}^3)Pa\\ & =& \left(4V_1\right)(100\times {10}^3)Pa\\ & & \end{array}$

Here work done energy is 80J

So the value of is$V_1=\left(\frac{80}{400\times {10}^3}\right)=200c{m}^3$