# Need help with calculating a Cv in PHYWE's Heat Capacity of gases

## Homework Statement:

-Calculating a Cv from the given equation and data , if everything goes right you'll obtain Cv=26 J*K^-1*mol^-1 as a result.

## Relevant Equations:

$$C_{V}=\frac{p_{0} V_{0}}{T_{0}} \cdot\left(\frac{U \cdot I \Delta t}{(a p+V) \cdot \Delta p}-\frac{a p}{a p+V}\right)$$
I've conducted this experiment yesterday. The main goal of this experiment is to find a gas constant R and compare it with its theoretical counterpart but I get stuck in calculating a Cv so I tried to find out what's wrong with my calculations by trying to calculate a Cv from the given data.

......(1)

where p0 = 1013 hPa , T0=273.2 K , V0 = 22414 ml/mol
U = 4.75 V , I = 0.25 A
a = 0.855 cm^3/hPa
p = 0.147 hPa
V = 1.14 L = 1140 mL
delta(p)/delta(t) = 1.67 hPa/s or delta(t)/delta(t) = 0.5988 s/hPa

If everything goes right I'll obtain Cv = 26 J*K-1*mol^-1 as a result

My attempt :

.........(2)
.....(3)

Plugged all the given values into the eq(2) and I got 42.67 instead of 26.

What is wrong with my calculation? , could someone please shed some light on this?

Here this is the documentation : https://www.nikhef.nl/~h73/kn1c/praktikum/phywe/LEP/Experim/3_2_02.pdf (page 4 and 5)

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mjc123
Homework Helper
Are your units consistent? Try converting everything to SI units.

TechieDork
Are your units consistent? Try converting everything to SI units.
I have tried a dimensional analysis with my units and yes....they are indeed consistent in the form of (J*K^-1*mol^-1).

I tried converting all of them to their SI units and plugged them in the equation but the result doesn't get anywhere near 26.
I think I'm getting stuck in the endless loop now. Could anyone please show me how?

Last edited:
Lord Jestocost
Gold Member
I think you are mistaking ##p## and ##\Delta p## and and are substituting the wrong value for ##p##. According to the documentation, ##p=1011~\rm{hPa}## (see page 5).

You're right,p was indeed equal to 1011 hPa, although, they wrote that this part of the experiment was performed in another day, (probably in other terms) so that value of p is invalid, he should calculate the formula with p's original value.