Question

A gas following the $pV$trajectory of FIGURE $EX21.12$does $60J$of work per cycle. What is $p_{max}$?

Short answer

The value of$p_{max}=300kPa$.

Step-by-step solution

Step: 1 Definition of pmax:

In case of varying pressure and volume , work done by a gas can be calculated by calculating the area of P-V curve . In case of triangle area of triangle can be calculated by the following formula .

$A=\frac{1}{2}\times b\times h$

A is area , b is length of base and h is height of triangle.

Step: 2 Finding the value of pmax:

The area enclosed by the graph is equal to the work done by the gas. That example, if we allow the maximum pressure value to be in $kPa$, as the figure is a triangle, we have

$W_{out}=\frac{\left(p_{max}-100\right)\cdot {10}^3\cdot (800-200)\cdot {10}^{-6}}{2}$

$$\begin{gathered} p_{max}-100=\frac{2W_{\text{out}}}{6\cdot {10}^{-1}} \\ \Rightarrow p_{max}=\frac{2W_{\text{out}}}{6\cdot {10}^{-1}}+100\mathrm{kPa}. \end{gathered}$$

Step: 3 Calculation:

We can substitute the value and calculate as follows.

$$\begin{gathered} p_{max}=\frac{2\times 60}{0.6}+100 \\ {p}_{max}=300\mathrm{kPa}. \end{gathered}$$