Calculating Heat Transfer to Ideal Gas During Isochoric Process

[rammer]

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?

 

[256bits]

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.

 

[rammer]

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]

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

 

[PJC01]

To calculate the heat transfer to an ideal gas during an isochoric process, you can use the first law of thermodynamics, which states that the change in internal energy (dU) of a system is equal to the heat transfer (dQ) minus the work done (dW). In an isochoric process, the volume remains constant, so there is no work done.

As you mentioned, the change in internal energy can be calculated using the equation dU = n*c*dT, where n is the number of moles of gas, c is the specific heat capacity of the gas, and dT is the change in temperature. However, as you have stated, the change in temperature is unknown.

In order to find the change in temperature, you will need to know the initial and final temperatures of the gas. This information can be obtained by knowing the initial and final pressures and volume, as well as the ideal gas law, which states that PV = nRT. By rearranging this equation, you can solve for the initial and final temperatures.

Once you have the initial and final temperatures, you can calculate the change in temperature (dT) and use it in the equation dU = n*c*dT to find the heat transfer (dQ).

It is not necessary to know the entire cycle (closed loop) in order to calculate the heat transfer in an isochoric process. However, having more information about the system and the process can help in making more accurate calculations.