Understanding the Ideal Gas Law: State Changes and Work Calculation | Geocities

[willydavidjr]

The diagram below shows state changes of an ideal gas. The temperature of states (1), (2), (3) are $$T_1[K], T_2[K]$$ and $$T_3[K]$$ respectively. The state change from (1) to (2) is an adiabatic change (not an isothermal change). The state change from (2) to (3) is a change at constant pressure (isobaric change). The state change from (3) to (1) is a change at constant volume (isochoric change).

Question: 1.) Write the size relation between $$T_1, T_2, T_3$$.

2.) Let the quantity of the ideal gas be 1[mol] and let R[J/mol*K] denote the gas constant. Find the work which the gas did on the outside during the state change from (2) to (3).

My idea:
For number 1: If I will write the relation between the 3 Temperatures, I will follow the Ideal gas law PV=nKT. But n and K can be disable because it will act as a constant and it is the same gas used. So am I correct if I say $$T_1 < T_2 < T_3$$. Or it looks like $$T_1 > T_2$$ What do you say?


For number 2:
Is there work done for the gas outside during the state change?


Note: You can view the diagram on this website : http://www.geocities.com/willydavidjr/pvdiagram

 

[quantumdude]

Question: 1.) Write the size relation between $$T_1, T_2, T_3$$.

For number 1: If I will write the relation between the 3 Temperatures, I will follow the Ideal gas law PV=nKT. But n and K can be disable because it will act as a constant and it is the same gas used. So am I correct if I say $$T_1 < T_2 < T_3$$. Or it looks like $$T_1 > T_2$$ What do you say?

I agree with you that $T_3$ is the biggest one. To correctly order $T_1$ and $T_2$ you should note that for adiabatic processes, $VT^{\alpha}=constant$.

2.) Let the quantity of the ideal gas be 1[mol] and let R[J/mol*K] denote the gas constant. Find the work which the gas did on the outside during the state change from (2) to (3).

My idea:
For number 1: If I will write the relation between the 3 Temperatures, I will follow the Ideal gas law PV=nKT. But n and K can be disable because it will act as a constant and it is the same gas used. So am I correct if I say $$T_1 < T_2 < T_3$$. Or it looks like $$T_1 > T_2$$ What do you say?

There has to be, because the gas is expanding. What's the definition of work in terms of pressure and volume?

 

[willydavidjr]

Wait a minute Tom Mattson, I think we're wrong. The question number asked about the size relation. Are they talking about the volume or the amount of Temperatures? And on question number two, how can I find the work done(W=PV) if the given only is the number of moles and R constant?Thank you.

 

[quantumdude]

Willy,

I have no idea of what the "size relation" is. That term certainly isn't standard. I assumed that you knew what it meant, and so I took your word for it that it was an inequality involving the temperatures. If it is something else then you should say so.

 

[willydavidjr]

Ok thank you, I am sorry because that was the same sentence I have here, maybe its an inequality involving temperatures.

How about "Let the quantity of the ideal gas be 1[mol] and let R[J/mol*K] denote the gas constant. Find the work which the gas did on the outside during the state change from (2) to (3)."?

My problem about this is that the given are n and R. We have no detail for the P,V,T to get the Work=PV...How can I solve it?

 

[willydavidjr]

It seems that T1 and T2 are uqual?