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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.

User Omabena
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1 Answer

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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

User Cezar Augusto
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