Finding molar specific heat at constant pressure

[dinospamoni]

Homework Statement

Let 25.6 J of heat be added to a particular ideal gas. As a result, its volume changes from 41.0 to 82.0 cm3 while the pressure remains constant at 1 atm(= 101 kPa).
a) By how much did the internal energy of the gas change? -- 21.5 J got this part

b) What is the molar specific heat at constant pressure?

c) Find the molar specific heat at constant volume.

d) For this gas, what is the effective number of degrees of freedom? (may not be an integer)

Homework Equations

PV=nRT
ΔE= nC_vΔT
C_p = C_v + R
Q = nC_p ΔT

The Attempt at a Solution

I think I have a handle on everything except part b. I know I need to find the change in temperature and the moles of the gas, at least that's what I think. After part b is found, c is just C_p + R where R is 8.314 if i remember correctly. And part d is just C_p = ((f+2)k N_a)/2 where k is Boltzmann's constant and N_a is avagadro's number.
Any help is appreciated! Thanks!

 

[haruspex]

It sounds to me like it should have specified that it's one mole of the gas. Otherwise, I doubt there's enough information. But this is not not an area I'm strong on.

 

[dinospamoni]

That's what i was thinking too. I've reread the question about 20 times and there's still no mention.
What may be the solution is to just assume that there is one mol. Then the answer would be specific heat per mol

 

[ehild]

Answer b) symbolically: From the given data, you can calculate (nR)T₁ and (nR)T₂. You can find T₁ and T₂ in terms of nR.
The process is at constant volume, so the heat is equal to Q=C_pn(T₂-T₁).
C_P=(f/2+1)R. Substituting the expressions for T₁ and T₂, nR will cancel and you get f.

ehild