Mathematical model, work done on a gas

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Homework Help Overview

The discussion revolves around calculating the work done on a gas described by a pressure function P=e^(-v^2), where v represents volume. The task is to determine the work as the volume decreases from infinity to zero.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definition of work and its mathematical representation, suggesting integration of the pressure function over the specified limits. There are questions about the setup of the integral and the substitution of the pressure function into the work formula.

Discussion Status

The discussion includes various attempts to set up the integral for calculating work, with some participants providing expressions for the integral and others questioning the correctness of the limits and the function used. There is no explicit consensus on the final result yet.

Contextual Notes

Participants are working within the constraints of a homework problem, focusing on the mathematical formulation without providing a definitive solution or numerical outcome.

kid_123
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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.
 
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Use the definition for work.

dW = PdV

Integrate both sides.
 
so would it just be ∫e-v2 from ∞ to 0?
 
which gives -.886227 joules?
 
W = -fnInt(e^v^2, v, infinity, 0)

Seems like just need to set up that definite integral.
 
Norfonz said:
Use the definition for work.

dW = PdV

Integrate both sides.

W=∫v1v2PdV

∴W=∫0∞PdV

Would he just simply substitute his P in this formula?
 

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