Thermodynamics/ideal gas question

[doctordiddy]

Homework Statement

) An ideal monatomic gas is expanded from initial volume V1 = 1 L, P1 = 2 atm, and T1
= 300K to a volume V2 = 2 L and P2 = 1 atm. The expansion is performed along along a
straight line in the PV-diagram. It is then re-compressed isothermally to its original values
completing the cycle for a type of heat engine.
(a) Find the function P(V) describing the expansion.
(b) Find the function T (V) during the expansion.
(c) At which volume is the temperature a maximum Tmax and what is the volume Vm at this
maximum temperature, Tmax?
(d) What is the work done, the change in internal energy and the heat taken in during the
temperature increase T to Tmax?
(e) What are these values for the final part of the expansion Vm to V2?
(f) Find the efficiency.

Homework Equations

PV=nRT

The Attempt at a Solution

I am currently stuck on a) and b). I am not sure how to write a function for these, and what equation to use. I assume that we use PV=nRT to derive a function but I have no idea what to do. It would be really helpful if you could give me an example of a similar question where you have to derive an equation to get the function

Any help is appreciated.

Thanks!

 

[ehild]

Homework Statement

) An ideal monatomic gas is expanded from initial volume V1 = 1 L, P1 = 2 atm, and T1
= 300K to a volume V2 = 2 L and P2 = 1 atm. The expansion is performed along along a
straight line in the PV-diagram. It is then re-compressed isothermally to its original values
completing the cycle for a type of heat engine.
(a) Find the function P(V) describing the expansion.
(b) Find the function T (V) during the expansion.
(c) At which volume is the temperature a maximum Tmax and what is the volume Vm at this
maximum temperature, Tmax?
(d) What is the work done, the change in internal energy and the heat taken in during the
temperature increase T to Tmax?
(e) What are these values for the final part of the expansion Vm to V2?
(f) Find the efficiency.

Homework Equations

PV=nRT

The Attempt at a Solution

I am currently stuck on a) and b). I am not sure how to write a function for these, and what equation to use. I assume that we use PV=nRT to derive a function but I have no idea what to do. It would be really helpful if you could give me an example of a similar question where you have to derive an equation to get the function

Any help is appreciated.

Thanks!

What is the equation of a straight line in a plane in general?

ehild

 

[doctordiddy]

What is the equation of a straight line in a plane in general?

ehild

I'm not really sure what that means.

Is it y=x or Ax+By+C=0?

 

[ehild]

Which one is more general?

ehild

 

[doctordiddy]

Which one is more general?

ehild

ax+by+c=0

 

[ehild]

The volume V corresponds to x and the pressure P corresponds to y. And you know two points of the line aV+bP+C=0: (V1,P1)=1,2 and (V2,P2)=(2,1). Find the constants a,b,c.

 

[doctordiddy]

The volume V corresponds to x and the pressure P corresponds to y. And you know two points of the line aV+bP+C=0: (V1,P1)=1,2 and (V2,P2)=(2,1). Find the constants a,b,c.

sorry i am a bit confused as to where you get V corresponding to x and what the equation of the straight line has to do with this question. Can you explain what formula I use and why?

 

[ehild]

read the problem:

The expansion is performed along along a
straight line in the PV-diagram.

In the P-V diagram,the equation of a straight line is aV+bP+c=0.

ehild