Work done on a gas as volume decreases

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SUMMARY

The forum discussion focuses on calculating the work done on a gas as its volume decreases from infinity to zero, given the pressure function P=e-v². The work is derived using the differential work equation dW = PdV, leading to the integral W=∫0∞e-v²dV. The solution correctly identifies the Gaussian integral, resulting in W=(√π)/2, confirming the accuracy of the calculation.

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In a mathematical model, a gas is under a pressure of the form P=e-v2 (v is volume). Find the work (in Joules) done on the gas as its volume decreases from infinity to zero.



dW = PdV



Solution Attempt:
W=∫0e-v2dV

http://en.wikipedia.org/wiki/Gaussian_integral

Gaussian Integral=∫-∞e-x2dx=√∏

∴∫0e-v2dV

=(√∏)/2|0

W=(√∏)/2

Is this correct?
 
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