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  • An ideal gas undergoes cyclic process ABCDA as shown in given P- V diagram (Figure). The amount of work done by the gas is

An ideal gas undergoes the cyclic process ABCDA as shown in the given P-V diagram (Figure). The amount of work done by the gas is

a) 6P_{0}V_{0}

b) -2P_{0}V_{0}

c) +2P_{0}V_{0}

d) +4P_{0}V_{0}

 

Answers (1)

The answer is the option (b) =-2P_{0}V_{0}

Let P be the pressure of the gas in the cylinder, then the force exerted by the gas on the piston of the cylinder,

F=PA

n a small displacement of piston through DC, work done by the gas,

dW=F.dx=PAdx=PdV

∴ Total amount of work done 

\bigtriangleup W = \int dW = \int_{V_{i}}^{V_{f}} PdV = P (V_{f} - V_{i})

In a P−V diagram or indicator diagram, the area under the P−V curve represents work done.

W= Area under P−V diagram

According to the P−V diagram given in the question,

Work done in the process ABCD= Area of rectangle ABCDA

=AB×BC=(3V_{0}−V_{0})×(2P_{0}−P_{0})

=2V_{0}×P_{0}=2P_{0}V_{0}

Since, the cyclic process is anti-clockwise, work done by the gas is negative.

That is, −2P_{0}V_{0}. Hence there is a net compression in the gas.

Posted by

infoexpert24

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