- #1

- 10

- 0

## Homework Statement

A Gas is in a Volume V

_{0}= 1 Liter at Pressure p

_{0}= 3 bar.

- Isochoric Heating using the Heat Q
_{1}= 182 J, the pressure raises to p_{1}= 6.34 bar. - Gas is reset to inital state. Isobaric Heating using the Heat Q
_{2}= 546 J, the Volume increases to V_{2}= 3 Liter.

_{p}/C

_{V}. Calculate the degrees of freedom f.

## Homework Equations

pV = nRT

C

_{V}= ΔQ/ΔT (for first step)

C

_{p}= ΔQ/ΔT (for second step)

C

_{p}/C

_{V}= 1+ 2/f

and optionally

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?