How Does the Ideal Gas Law Apply to a Cylinder's Thermodynamic Cycle?

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The discussion focuses on applying the Ideal Gas Law to analyze a thermodynamic cycle involving a monatomic gas in a cylinder. Initially, the gas is at state A with known volume and pressure, and it undergoes an isobaric process to state B, where the pressure remains constant while volume increases. The gas then transitions to state C at constant volume, maintaining the same temperature as state A, prompting questions about pressure determination at state C. Participants express confusion about the relationships between pressure, volume, and temperature, particularly in the context of isothermal and isochoric processes, while also debating whether the system functions as a refrigerator or a heat engine. The discussion emphasizes the need to utilize the Ideal Gas Law and PV diagrams to clarify these thermodynamic relationships.
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Homework Statement


A cylinder contains 2 moles of an ideal monatomic gas that is initially at state A with a volume of 1.0 x 10^-2 m3 and a pressure of 4.0 x 10^5 Pa. The gas is brought isobarically to state B. where the volume is 2.0 x 10^-2 m3. The gas is then brought at constant volume to state C, where its temperature is the same as at state A. The gas is then brought isothermally back to state A.
a. Determine the pressure of the gas at state C.
b. State whether this device is a refrigerator or a heat engine. Justify your answer.

So here's my version of that,

n = 2mol
stateA
v = 1.0 x 10-2m3
p = 4.0 x 105 Pa
stateB
v = 2.0 x 10-2 m3
p = 4.0 x 105 Pa (Isobaric Process)
stateC
v = 2.0 x 10-2 m3 (Isochoric Process)
tc = ta
w = 0 (isochoric)
p = ?

Homework Equations


p=F/A?
w=pdeltav?

The Attempt at a Solution


a)i know that the fact tc = ta has something to do with this, but when i consider this i would get deltau to = 0 due to the isothermal process right? and if deltau = 0 then q=w then t=p.02? but then how would i solve for p if i don't know t? >_< this is confusing...
b)i know that if i made a pv graph for this id have something like A---->B then C directly under B but because i don't know the answer to question a i don't know exactly where, also does that even have anything to do with it? I am guessing that with less volume you have higher temperature and the opposite with lots of volume but then my teacher showed us that in carnot cycles its actually colder when there's less volume! i would have to say refrigerator just because at b; the only state where temperature changes it would increase becauseto maintain the same pressure at an increased volume you would have to have a higher temperature right?
 
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help please? :(
 
Div said:

The Attempt at a Solution


a)i know that the fact tc = ta has something to do with this, but when i consider this i would get deltau to = 0 due to the isothermal process right? and if deltau = 0 then q=w then t=p.02? but then how would i solve for p if i don't know t? >_< this is confusing...
b)i know that if i made a pv graph for this id have something like A---->B then C directly under B but because i don't know the answer to question a i don't know exactly where, also does that even have anything to do with it? I am guessing that with less volume you have higher temperature and the opposite with lots of volume but then my teacher showed us that in carnot cycles its actually colder when there's less volume! i would have to say refrigerator just because at b; the only state where temperature changes it would increase becauseto maintain the same pressure at an increased volume you would have to have a higher temperature right?
Use the ideal gas law and do a PV diagram.

The path from A to B is a horizontal line to the right a distance of V0 (1.0 x 10^-2 m^3) . What happens to T from A to B? (use Ideal Gas Law). Is heat flowing? What direction (into or out of the gas?).

The path from B to C is a vertical line. What is the pressure at C? (use Ideal Gas Law). Is heat flowing? Direction?

For the path from C to A, T is constant so how does P vary with V? (use Ideal Gas Law). Is CA a straight line? Curve? Is heat flowing? Direction?

What does the area between inside the path represent? Is it positive or negative? (you have to add the areas under each path - careful with signs). Is work being done by the gas or is work being on the gas?

AM
 

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