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Calculating a Cv in PHYWE's Heat capacity of gases experiment

Physics Asked by ToughCookie on December 20, 2020

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 in the documentation.

$$C_{V}=frac{p_{0} V_{0}}{T_{0}} cdotleft(frac{U cdot I Delta t}{(a p+V) cdot Delta p}-frac{a p}{a p+V}right)$$

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(p) = 0.5988 s/hPa

If everything goes right , I’ll obtain $$C_{V}=26 mathrm{J} cdot mathrm{K}^{-1} cdot mathrm{mol}^{-1}$$ as a final result.

My attempt:

$$C_{V}=frac{p_{0} V_{0}}{T_{0}} cdotleft(frac{1}{a p+V}right)left(frac{U cdot I Delta t}{Delta p}-mathrm{ap}right)$$

enter image description here

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

Plugged all the needed values in the equation and I got Cv=42.67 instead of 26.

Here this is the documentation (page 4 and 5)

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