Finding the heat transferred in an ininitesimal quasistatic process

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SUMMARY

The discussion focuses on deriving the expression for heat transferred in an infinitesimal quasistatic process for an ideal gas, represented by the equation dQ = (C_V/nR)VdP + (C_P/nR)PdV. Participants emphasize starting with the first law of thermodynamics, dQ = dU + PdV, and suggest using the relationship PV = nRT to find the differential dT. This approach is essential for understanding how heat capacity varies with the process type, whether at constant volume or pressure.

PREREQUISITES
  • Understanding of the ideal gas law (PV = nRT)
  • Knowledge of the first law of thermodynamics (dQ = dU + PdV)
  • Familiarity with heat capacities (C_V and C_P)
  • Basic calculus for handling differentials
NEXT STEPS
  • Study the derivation of the first law of thermodynamics in detail
  • Learn about the differences between heat capacities C_V and C_P
  • Explore the concept of quasistatic processes in thermodynamics
  • Investigate the relationship between temperature changes and work done in thermodynamic systems
USEFUL FOR

This discussion is beneficial for students of thermodynamics, physicists, and engineers who are looking to deepen their understanding of heat transfer in ideal gases during quasistatic processes.

Narcol2000
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For an ideal gas PV=nRT where n is the number of moles show that the heat transferred can be written as:

[tex] dQ = \frac{C_V}{nR}VdP + \frac{C_P}{nR}PdV[/tex]

Really not sure where to start with this...

I have used

[tex] dQ = dU + PdV[/tex]

But it hasn't really lead anywhere.
 
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Narcol2000 said:
For an ideal gas PV=nRT where n is the number of moles show that the heat transferred can be written as:

[tex] dQ = \frac{C_V}{nR}VdP + \frac{C_P}{nR}PdV[/tex]

Really not sure where to start with this...

I have used

[tex] dQ = dU + PdV[/tex]

But it hasn't really lead anywhere.
Start with:

dQ = mCdT where C is the heat capacity of the gas. (The heat capacity, of course, depends on whether the gas does work as the heat flows into the gas, so it does not have a fixed value).

Using PV = nRT, what is dT? That should get you going in the right direction.

AM
 

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