Mathematical model, work done on a gas

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To find the work done on a gas under the pressure model P=e-v² as its volume decreases from infinity to zero, the work can be calculated using the formula dW = PdV. The integral to evaluate is W = ∫ from 0 to ∞ of e-v² dV. This results in a value of approximately -0.886227 joules. The discussion emphasizes the need to correctly set up the definite integral and substitute the pressure function into the formula for work. The final answer confirms the integration process and the substitution of P into the work equation.
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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