Change in heat and internal energy

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Homework Help Overview

The discussion revolves around the concepts of heat transfer and internal energy changes in thermodynamics, particularly in the context of an ideal gas undergoing a full cycle. Participants are exploring the implications of different heat capacities and the relationship between work done and changes in internal energy.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning whether the heat capacity should be Cp or Cv due to the nature of the process involving both pressure and volume changes. There is also a discussion about calculating work done and its relation to internal energy changes, with references to specific formulas and conventions.

Discussion Status

The discussion is active, with participants providing insights into the relationships between work, heat, and internal energy. Some guidance has been offered regarding the calculation of work and the implications of the ideal gas law, but no consensus has been reached on the specific heat capacity to use in this context.

Contextual Notes

Participants are navigating the complexities of a thermodynamic cycle, noting that the system returns to its initial state, which raises questions about the overall change in internal energy. There is an emphasis on ensuring that the signs of calculated values align with the chosen sign convention.

Ashshahril
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Homework Statement
What is the change in heat and internal energy in this PV diagram (attached link) from T2 to T3 (T represents temperature)?
Relevant Equations
ΔQ=mC(T3-T1)
Δu=ΔQ + Δw
ΔQ=mC(T3-T1)

But, will this C be Cp or Cv. Both pressure and volume changes. So, neither of them can be.

Feeling so confused
 

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Calculate the work from 2-3 which will be the area under the line from 2-3( trapezium area) and you know the change in internal energy= Cv(T2-T3) and u will get ∆Q
 
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Note this is a full cycle. You start at point 1 and finish at point 1. So the system's final state is the same as its initial state. What can you say about the overall change in the system's internal energy, ΔU?

The area gives you the work done by the gas. ΔW:
https://www.ux1.eiu.edu/~cfadd/1150/14Thermo/Images/Diag10.gif
If you are dealing with n moles of an ideal gas you can use PV = nRT to get the value of V at each vertex and then derive a formula for ΔW in terms of the P's, T's, n and R.

Then you can find ΔQ.

Make sure the signs (+ or -) of your answers match the sign-convention you are using.

Edit: poor wording corrected.
 
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For an ideal gas, internal energy is a function only of temperature. By definition, Cv is given by $$mC_v=\left(\frac{\partial U}{\partial T}\right)_V$$But, since U is dependent only on T for an ideal gas, $$\Delta U=mC_v\Delta T$$
 
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