Question

A gas in a piston-cylinder device is compressed such that the pressure-volume trajectory follows a polytropic path, p1V1^n = p2V2^n. The subscripts 1 and 2 indicate the beginning and end of the process. Where n = 1.3. If the initial pressure is 1 bar and the initial volume is 1 m^3, and the final volume is 0.1 m^3, calculate the work done on the gas. Give your answer in kJ.

          A gas in a piston-cylinder device is compressed such that the pressure-volume trajectory follows a polytropic path, p1V1^n = p2V2^n. The subscripts 1 and 2 indicate the beginning and end of the process. Where n = 1.3. If the initial pressure is 1 bar and the initial volume is 1 m^3, and the final volume is 0.1 m^3, calculate the work done on the gas. Give your answer in kJ.
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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A gas in a piston-cylinder device is compressed such that the pressure-volume trajectory follows a polytropic path, p1V1^n = p2V2^n. The subscripts 1 and 2 indicate the beginning and end of the process. Where n = 1.3. If the initial pressure is 1 bar and the initial volume is 1 m^3, and the final volume is 0.1 m^3, calculate the work done on the gas. Give your answer in kJ.
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Transcript

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00:01 In this video we are going to be finding the integration for each case.
00:09 So we're going to take the formula p1 times p.
00:17 Oops, v1.
00:21 It's going to be equal to p2 times v2, and it's going to be to the nth power.
00:33 And we want to solve for p.
00:36 So p1 is going to be equal to p2 times v2 1, 3 1, the nth power.
00:54 So we're going to input our knowns, much for pressure 2, it's going to be 200...
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