# Thermo Chemistry: Explaining Cp vs Cv

• zorro
In summary, the heat capacity at constant pressure, Cp, is typically larger than that at constant volume, Cv, because at constant pressure, some of the added heat can be used for expanding the substance while at constant volume, all of the added heat goes towards increasing the temperature. This may be confusing because at constant volume, the heated gas wants to expand but is unable to, leading to an increase in pressure. There is no difference between expansion and inflation of gas in this context.
zorro
This is a statement in my book 'The heat capacity at constant pressure Cp is generally larger than that at constant volume Cv because at constant pressure, a part of heat added to the substance may be used in work of expanding whereas at constant volume all the added heat produces a rise in temperature'. I did not understand these two things-

At constant pressure, how can heat added be used for expanding (since expanding leads to change in pressure).

At constant volume what if the added heat expands the gas?

If you heat something it usually inflates, to keep the pressure constant it has to expand.

In constant volume heated gas WANTS to expand - but as the volume is kept constant, it is impossible, so instead the pressure goes up.

--

what is the difference between expansion and inflation of gas?

None as far as I am concerned, sorry if it sounded as there is a difference.

I can explain the concept of Cp (specific heat capacity at constant pressure) and Cv (specific heat capacity at constant volume) in more detail. Let's start with the definition of specific heat capacity - it is the amount of heat required to raise the temperature of a substance by 1 degree Celsius (or Kelvin) per unit mass.

Now, at constant pressure, the substance is allowed to expand as it absorbs heat. This expansion leads to an increase in volume, but the pressure remains constant. The heat added to the substance is used for both increasing the temperature and doing work (expansion). This means that the substance needs more heat to increase its temperature by 1 degree Celsius compared to when it is at constant volume. Therefore, Cp is generally larger than Cv at constant pressure.

Now, let's consider the case of constant volume. Here, the substance is not allowed to expand, so all the heat added is used only for increasing the temperature. However, in this case, if the substance is a gas, the added heat can cause the gas molecules to move faster and increase the pressure. This increase in pressure will result in the substance needing more heat to increase its temperature by 1 degree Celsius. Therefore, even at constant volume, the specific heat capacity will be slightly larger than at constant pressure for gases.

In summary, at constant pressure, some of the added heat is used for work (expansion) and at constant volume, the added heat can still lead to an increase in pressure. This is why Cp is generally larger than Cv. I hope this explanation helps you to understand these concepts better.

## 1. What is the difference between Cp and Cv in thermochemistry?

Cp and Cv are both thermodynamic properties that describe the heat capacity of a substance. However, they differ in the conditions under which they are measured. Cp is measured at constant pressure, while Cv is measured at constant volume.

## 2. Why is Cp considered to be the more practical heat capacity measurement?

Cp is considered more practical because most chemical reactions occur at constant pressure, making it a more relevant measurement in real-world applications. It also accounts for the work done by the system during a reaction, which is typically negligible in comparison to heat exchange.

## 3. How do Cp and Cv relate to each other?

Cp and Cv are related by the following equation: Cp = Cv + R, where R is the gas constant. This shows that Cp is always greater than Cv, as it takes into account the additional heat required to do work at constant pressure.

## 4. Can Cp and Cv vary for different substances?

Yes, Cp and Cv can vary for different substances due to differences in molecular structure and intermolecular forces. For example, substances with stronger intermolecular forces tend to have higher heat capacities because they require more energy to change their temperature.

## 5. How are Cp and Cv used in thermodynamic calculations?

Cp and Cv values can be used in thermodynamic equations to calculate changes in energy, temperature, and volume during a reaction. They can also be used to determine the enthalpy and entropy of a substance, which are important factors in understanding chemical reactions and thermodynamic processes.

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