Mathematical model, work done on a gas

AI Thread Summary
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
Messages
5
Reaction score
0
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.
 
Physics news on Phys.org
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?
 

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Confusion about work done by a gas - Thermodynamics
Replies
15
Views
1K
Calculating Work Done by Gas at Constant Pressure
Replies
2
Views
2K
Work done in a chamber with gas undergoing adiabatic free expansion?
Replies
13
Views
2K
Calculating ΔE Difference for 2 Samples of Monatomic Ideal Gas
Replies
4
Views
2K
How Is Work Calculated for a Gas and Balloon in Isothermal Expansion?
Replies
11
Views
4K
Work done on container receiving gas from high pressure container
Replies
1
Views
1K
Help Calculate Work Done in Adiabatic Process & Fill Table
Replies
19
Views
2K
Is enthalpy just the sum of internal energy and work against external pressure?
Replies
5
Views
990
Work done BY the gas in a cyclic thermodynamic process
Replies
2
Views
2K
Isothermal, isobaric and adiabatic
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top