Calculating Heat Transfer to Ideal Gas During Isochoric Process

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    Gas Ideal gas
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Discussion Overview

The discussion focuses on calculating heat transfer to an ideal gas during an isochoric process, exploring the relationships between pressure, volume, and temperature without needing to know the entire thermodynamic cycle.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the calculation of heat transfer during an isochoric process, noting the known initial and final pressures and volume but expressing uncertainty about temperature changes.
  • Another participant emphasizes the importance of specifying whether to use molar heat capacity at constant pressure (Cp) or constant volume (Cv) and suggests using the ideal gas equation, PV=nRT, as a starting point.
  • A participant specifies using Cv for a monoatomic ideal gas, stating that Cv=3/2 R, and derives an expression for heat transfer (Q) based on changes in pressure and volume.
  • There is a correction from another participant regarding the final equation, indicating that an R is missing in the derived expression and suggesting a more general form that applies to any ideal gas.

Areas of Agreement / Disagreement

Participants generally agree on the approach to calculating heat transfer, but there are differing views on the completeness and correctness of the final derived equation.

Contextual Notes

Some assumptions about the ideal gas behavior and the specific heat capacities are made, but the discussion does not resolve the implications of these assumptions or the accuracy of the derived equations.

rammer
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How to calculate heat transfer to an ideal gas during isochoric process? I only know initial and final pressures and volume. (Do I have to know whole cycle (closed loop)?)

Here, no work is done so:

dU = dQ
n*c*dT=dQ

But T and its change is unknown, so what would be the next step?
 
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You should specify which C you are using Cp or Cv, as each ahs a spcific value.

Also have you heard of the ideal gas equation, PV=nRT?
That is the hint to get you started to the next step.
 
As molar heat capacity I use "cv". Let's say an ideal gas is monoatomic, so "cv"=3/2 R.

I involved equation pv=nRT as you suggested and figured something out:

dU = dQ
n*cv*dT=dQ
∫n*cv*dT=∫dQ
n*cv*ΔT = Q

------
p*V = n*R*T
dp*V + p*dV = n*R*dT (isobaric p. dV=0)
∫dp*V = ∫n*R*dT
Δp*V = n*R*ΔT
ΔT = Δp*V / (n*R)
------

After substituting ΔT into the first integrated equation:

Q = 3/2 *VΔp

I got rid out of T and it seems correct, is it?
 
Perfect firugring out !
But, you are missing an R in your final equation

In any case, you could just leave as:
Q = ( Cv/R ) V Δp
and that would work for any ideal gas, momoatomic, diatomic, ... polyatomic
 

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