Question

A gas in a piston-cylinder asscmbly undcrgocs a process for which the rclationship bctwcen pressurc and volumc is pV^2=constant The initial pressurc is 1 bar, the initial volume is 0.4 m^3, and the final pressure is 9 bar. Determine the work for the process, in kJ constant.

Answer 1

Given:

`pV^(2)` = constant (1)

⇒
`p_(1)V_(1)^(2) = p_(2)V_(2)^(2)` (2)

`p_(1) = 1 bar = 1* 10^(5)`

`p_(2) = 9 bar = 9* 10^(5)`

`V_(1) = 0.4 m^(3)`

`V_(2) = ? m^(3)`

Solution:

Here, from eqn (1), the polytropic constant is '2' ( Since, here
`pV^(n)` =
`pV^(2)` )

Now, using eqn (2), we get

`V_(2)^(2) =(p_(2))/(p_(1))* V_(1)^(2)`

putting the values in above eqn, we get-

`V_(2)^(2) =(9)/(1)* 0.4^(2)`

`V_(2) = 1.2 m^(3)`

Now, work for the process is given by:

`W = (p_(2)V_(2) - p_(1)V_(1))/(1 - n)` (3)

where,

n = potropic constant = 2

Using Eqn (3), we get:

`W = (9* 10^(5)* 1.2 - 1* 10^(5)* 0.4)/(1 - 2)`

W = - 240 kJ