# Ideal gas processes

## Main Question or Discussion Point

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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256bits
Gold Member
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?

256bits
Gold Member
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