Help with thermodynamics -- work of Carnot engine expansion

[nate9519]

Homework Statement

I don't need help solving I just need some clarification. Since the carnot cycle is adiabatic, the first law would reduce to work= mass*(change in internal energy). On my test I was asked to calculate the work of the isentropic expansion of a carnot engine with air as the working fluid. I got confused and calculated from step 1-3( isothermal expansion and isentropic expansion) instead of 2-3( just isentropic expansion.) But since step 1-2 is isothermal would that mean the change in internal energy from 1-3 is the same as 2-3 meaning I would still have gotten the right answer

Homework Equations

The Attempt at a Solution

 

[Chestermiller]

Homework Statement

I don't need help solving I just need some clarification. Since the carnot cycle is adiabatic, the first law would reduce to work= mass*(change in internal energy). On my test I was asked to calculate the work of the isentropic expansion of a carnot engine with air as the working fluid. I got confused and calculated from step 1-3( isothermal expansion and isentropic expansion) instead of 2-3( just isentropic expansion.) But since step 1-2 is isothermal would that mean the change in internal energy from 1-3 is the same as 2-3 meaning I would still have gotten the right answer

Homework Equations

The Attempt at a Solution

Sure.

 

[Chandra Prayaga]

Homework Statement

I don't need help solving I just need some clarification. Since the carnot cycle is adiabatic, the first law would reduce to work= mass*(change in internal energy). On my test I was asked to calculate the work of the isentropic expansion of a carnot engine with air as the working fluid. I got confused and calculated from step 1-3( isothermal expansion and isentropic expansion) instead of 2-3( just isentropic expansion.) But since step 1-2 is isothermal would that mean the change in internal energy from 1-3 is the same as 2-3 meaning I would still have gotten the right answer

Homework Equations

The Attempt at a Solution

I need some clarification of the steps involved here. You were asked to calculate the Work during the isentropic expansion (2 - 3). You are saying the change in internal energy from 1 - 3 is the same as the change in internal energy from 2 - 3. I agree with your statement, but how is it related to the work? Your statement: "Since the carnot cycle is adiabatic, the first law would reduce to work= mass*(change in internal energy)." is very confusing. Are you talking about the entire Carnot cycle (1 - 2 - 3 - 4 - 1)? The entire cycle is not adiabatic, and the total change in internal energy for the entire cycle is zero, and that is not related to the work done.

 

[nate9519]

sorry for confusion. No I didn't mean the entire cycle is adiabatic. I meant from 2-3. My book uses a piston cylinder to demonstrate the carnot cycle and since that is a closed system I thought the first law reduces to mass*(change in internal energy) for the work from 2-3

 

[Chandra Prayaga]

OK. So the work from 2-3 (adiabatic expansion) needs to be calculated independently. It is still equal to the negative of the change in internal energy, because the heat input is zero.

 

[nate9519]

yes and that would give you an answer in kilojoules per unit mass. But the problem stated that the working fluid was 15kg of air so if I multiplied delta u by 15kg to get the answer in kJ that would be correct as well, right?

 

[Chandra Prayaga]

Make sure that the internal energy is calculated in the same units. Both the quantities, change in internal energy and work must come out in kJ.