A Gas is in a Volume V0 = 1 Liter at Pressure p0 = 3 bar.
- Isochoric Heating using the Heat Q1 = 182 J, the pressure raises to p1 = 6.34 bar.
- Gas is reset to inital state. Isobaric Heating using the Heat Q2 = 546 J, the Volume increases to V2 = 3 Liter.
pV = nRT
CV = ΔQ/ΔT (for first step)
Cp = ΔQ/ΔT (for second step)
Cp/CV = 1+ 2/f
U = ΔQ + ΔW = f/2 n R T
The Attempt at a Solution
The task as described above is pretty straightforward and yields the expected f = 3 solution.
However, I thought about another way of solving this exercise, but it keeps on yielding different results:
If I take the last equation (Joules Law: U = f/2 n R T) together with the ideal Gas Equation for the isochoric process, I get f = 1.09. (Again straightforward inserting and solving for f.)
Those results don't match. Neither do they, if I take the isobaric process (taking into account, that work is done). Just by taking the quotient of those two, I get the expected result. Is this a flaw in the exercise or is there any mistake within my formulas?