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

• TechieDork
In summary, the conversation discusses an experiment conducted to find a gas constant and compare it with its theoretical counterpart. The individual gets stuck in calculating a Cv and seeks help in finding the error in their calculations. They mention the given data and the equation used, and discuss converting units to SI units. They also mention a possible error in substituting the wrong value for a variable.
TechieDork
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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Last edited:
Are your units consistent? Try converting everything to SI units.

TechieDork
mjc123 said:
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:
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.

## 1. What is Cv and why is it important in calculating heat capacity of gases?

Cv, also known as specific heat at constant volume, is a measure of the amount of heat required to raise the temperature of a substance by one degree Celsius at constant volume. It is an important factor in calculating the heat capacity of gases because it provides information about how much heat is needed to change the temperature of a gas without changing its volume.

## 2. How do I calculate Cv for a gas using PHYWE's Heat Capacity of gases experiment?

To calculate Cv for a gas using PHYWE's experiment, you will need to measure the change in temperature and the change in internal energy of the gas. Then, you can use the formula Cv = ΔU/ΔT, where ΔU is the change in internal energy and ΔT is the change in temperature.

## 3. What units are used for Cv in PHYWE's Heat Capacity of gases experiment?

In PHYWE's experiment, Cv is typically measured in joules per mole per Kelvin (J/mol·K). However, it can also be expressed in other units such as calories per mole per Kelvin (cal/mol·K) or kilojoules per kilogram per Kelvin (kJ/kg·K).

## 4. How does the value of Cv differ for different gases?

The value of Cv can vary for different gases due to differences in their molecular structure and composition. For example, monatomic gases such as helium have a lower Cv compared to diatomic gases like nitrogen, which have more complex molecular structures. This is because more complex molecules have more degrees of freedom, meaning they can store more energy and require more heat to raise their temperature.

## 5. Can Cv be used to determine the specific heat of a gas at constant pressure?

No, Cv is specifically for measuring the specific heat at constant volume. To determine the specific heat at constant pressure, you will need to use the formula Cp = Cv + R, where Cp is the specific heat at constant pressure and R is the gas constant. This takes into account the work done by the gas as it expands at constant pressure.

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