Work done on a gas as volume decreases

In summary, work done on a gas as volume decreases refers to the energy transferred to or from a gas as its volume is reduced. It can be calculated by multiplying external pressure by the change in volume and is closely related to the transfer of heat. The work done on a gas can be either positive or negative depending on the direction of the change in volume. Some real-world examples include compressing air in a bicycle pump, car engine, and scuba tank.
  • #1
kabailey
17
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.



dW = PdV



Solution Attempt:
W=∫0∞e-v2dV

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

Gaussian Integral=∫-∞∞e-x2dx=√∏

∴∫0∞e-v2dV

=(√∏)/2|∞0

W=(√∏)/2

Is this correct?
 
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  • #2
anybody?
 

1. What is meant by work done on a gas as volume decreases?

Work done on a gas as volume decreases refers to the energy that is transferred to or from a gas as its volume is reduced. This can happen through compression, where external forces are used to decrease the volume of the gas, or through expansion, where the gas expands and does work on its surroundings.

2. How is work calculated in this scenario?

Work done on a gas as volume decreases can be calculated by multiplying the external pressure by the change in volume. This formula, W = PΔV, is known as the work-energy theorem and is based on the fact that energy and work are equivalent.

3. What is the relationship between work and heat in this process?

In this scenario, work done on a gas as volume decreases is closely related to the transfer of heat. When a gas is compressed, the molecules are forced closer together, increasing their kinetic energy and temperature. This increase in temperature is equivalent to the work done on the gas.

4. Is the work done on a gas always positive when the volume decreases?

No, the work done on a gas can be either positive or negative depending on the direction of the change in volume. If the gas is being compressed, the work done on it will be positive since energy is being transferred to the gas. If the gas is expanding, the work done on it will be negative since the gas is doing work on its surroundings.

5. What are some real-world examples of work done on a gas as volume decreases?

Some examples of work done on a gas as volume decreases include the compression of air in a bicycle pump, the compression of gases in a car engine, and the compression of air in a scuba tank. In all of these scenarios, external forces are used to decrease the volume of the gas, resulting in work being done on the gas.

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