Answer to Question #284560 in Mechanical Engineering for lala

Question

A quantity of a fluid with an initial pressure of 500KPa and an initial volume of 1m3 is made to undergo as process w/in a piston-cylinder system, Compute the work done by the fluid according to the condition that pressure is proportional to the square of volume. Express your answer in J.

Answer 1

Determine how exactly pressure depends on volume:

$$P(v)=kv^2,\\\space\\ 500000=k·1^2,\\\space\\ k=500·10^3$$

The work is

$$W=\int^{V_2}_{V_1}P\text dv=\int^{2}_{1}kv^2\text dv=\dfrac13kv^3,\\\space\\ W=500·10^3·\dfrac13(2^3-1^3)=1166667\text{ J}.$$