Thermodynamics - Ideal gas expansion

In summary, the problem involves an ideal gas expanding at a constant temperature to four times its initial volume, with 2.1E5 J of heat entering. Using the equation Q = W for an isothermal process, we can express W in terms of n, T, and Vi and Vf. With values for T and Vf/Vi, we can then solve for n using the ideal gas equation.
  • #1
Chase11
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Homework Statement


2.1E5 J of heat enters an ideal gas as it expands at a constant T = 77°C to four times its initial volume. How many moles of gas are there?

T=350K, Q=2.1E5 J, Vi=x, Vf=4x

Homework Equations


ΔU=Q-W
W=[itex]\int[/itex]pdV
U=nCvT

The Attempt at a Solution



I'm not sure if I'm even on the right track here.
I have W=[itex]\int[/itex]pdV = nRT[itex]\int[/itex]dv/V = nRTln(Vf-Vi)
I am stuck here because I need to know n to solve for work but I need to know W to solve for n. I am clearly missing something but I can't figure out what it is.
 
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  • #2
Chase11 said:

Homework Statement


2.1E5 J of heat enters an ideal gas as it expands at a constant T = 77°C to four times its initial volume. How many moles of gas are there?

T=350K, Q=2.1E5 J, Vi=x, Vf=4x


Homework Equations


ΔU=Q-W
W=[itex]\int[/itex]pdV
U=nCvT

The Attempt at a Solution



I'm not sure if I'm even on the right track here.
I have W=[itex]\int[/itex]pdV = nRT[itex]\int[/itex]dv/V = nRTln(Vf-Vi)
I am stuck here because I need to know n to solve for work but I need to know W to solve for n. I am clearly missing something but I can't figure out what it is.
You are given Q. What is the relationship between Q and W if the process is isothermal?

AM
 
  • #3
Yes thank you I realized yesterday that Q=W for an isothermal process. However I was still stuck after that. I feel like I should just use the ideal gas equation but I can't do that since I don't know pressure.
 
  • #4
Chase11 said:
Yes thank you I realized yesterday that Q=W for an isothermal process. However I was still stuck after that. I feel like I should just use the ideal gas equation but I can't do that since I don't know pressure.
Express W in terms of n, T and Vi and Vf (check your equation for W - your integration is not correct). You have values for T, and Vf/Vi. If Q = W, express n in terms of Qm T, Vf/Vi

AM
 
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  • #5


You are on the right track, but there is a simpler approach to solve this problem. Since the gas is expanding at a constant temperature, we can use the ideal gas law to relate the initial and final volumes:

P1V1 = P2V2

Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. We can rearrange this equation to solve for the final volume:

V2 = (P1V1)/P2

Substituting in the given values, we get:

V2 = (1 atm * x)/4 atm = x/4

Now, we can use the ideal gas law again to relate the number of moles to the volume:

n = (PV)/(RT)

Substituting in the given values and the final volume we calculated, we get:

n = (1 atm * x/4)/(0.0821 L*atm/mol*K * 350 K) = 0.000286 mol

Therefore, there are 0.000286 moles of gas in the system.
 

1. What is an ideal gas expansion?

An ideal gas expansion refers to the process of converting potential energy stored in a compressed gas into kinetic energy as it expands. This expansion is governed by the laws of thermodynamics and can be used to do work.

2. What are the main factors that affect ideal gas expansion?

The main factors that affect ideal gas expansion are the initial temperature, pressure, and volume of the gas, as well as the work done on or by the gas during the expansion process.

3. How is the work done during an ideal gas expansion calculated?

The work done during an ideal gas expansion can be calculated using the equation W = PΔV, where W is the work done, P is the pressure, and ΔV is the change in volume of the gas.

4. What is the ideal gas law and how is it related to ideal gas expansion?

The ideal gas law, also known as the equation of state, is PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. This law is related to ideal gas expansion as it describes the relationship between pressure, volume, and temperature for an ideal gas during the expansion process.

5. What are some real-world applications of ideal gas expansion?

Ideal gas expansion has many practical applications, such as in internal combustion engines, refrigeration systems, and gas-powered turbines. It is also used in industrial processes for producing energy and in the production of chemical reactions.

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