# How Does Potential Energy Affect the Internal Energy of Real Gases?

• themanonthemo
In summary, The conversation discusses the concept of internal energy in ideal and real gases, and the confusion surrounding the relationship between potential energy and pressure or volume. It is explained that for ideal gases, the internal energy is solely dependent on temperature, while for real gases it also takes into account potential energy. However, the exact relationship between potential energy and pressure or volume is not straightforward and can vary depending on the specific conditions.
themanonthemo
Hello everybody.

The concept of internal energy of a real vs ideal gas has perplexed me.
From what I understand, an ideal gas solely considers the kinetic energy of gas molecules (temperature) where as real gases consider kinetic energy of particles in addition to potential energy.

So logically this would be true..

ideal: U = 1.5nRT (for a monatomic gas) real: U = 1.5nRT + PE (for a monatomic gas)
from what I read from the textbook, PE is a function of Pressure or volume.

Next, the idea of heat capacities seems strange. It is said that
dQ = (n)(Cv)(dT) where Cv is the heat capacity at constant volume.

For an ideal gas at const. volume or NOT: it is logical that Cv would be 1.5R (assuming a monatomic gas)

Question: For a real gas at const volume, the formula dU = nCvdT apparently still applies, although Cv is not idealized like in the previous example.

dU = dKE + dPE (real gas) nCvdT = n(1.5R)dT + dPE dPE = ndT(Cv - 1.5R)

This suggests that PE is only a function of temperature which contradicts the idea that it is a function of pressure or volume.

Is there something wrong with my assumptions?

I'm sorry if it's not clear. I appreciate all the help!

themanonthemo said:
This suggests that PE is only a function of temperature which contradicts the idea that it is a function of pressure or volume.
If V is constant, isn't here a relationship between T and P? Also, the value of ##C_V## can be different depending on which range of pressure you are considering.

The potential energy in a real gas basically depends on the average distance between molecules, and not in a linear fashion. Therefore, any things that changes this distance will affect the internal energy of a gas, and that is the reason why you normally do not get a simple relation between the internal energy and the temperature alone.

## 1. What is internal energy of a real gas?

The internal energy of a real gas is the sum of all the kinetic and potential energies of its molecules. It includes both the translational, rotational, and vibrational energies of the molecules. In other words, it is the total energy that a gas possesses due to the movement and interactions of its particles.

## 2. How is the internal energy of a real gas different from an ideal gas?

An ideal gas is a theoretical concept that assumes no intermolecular forces and no volume for its particles. Therefore, the internal energy of an ideal gas is solely dependent on the kinetic energy of its particles. On the other hand, a real gas has intermolecular forces and occupies a volume, which contributes to its internal energy.

## 3. What factors affect the internal energy of a real gas?

The internal energy of a real gas is affected by several factors, including temperature, pressure, volume, and the type of gas. An increase in temperature will increase the internal energy as the molecules have more kinetic energy. Higher pressure and smaller volume also tend to increase the internal energy as the molecules are closer together and have more interactions.

## 4. How is the internal energy of a real gas measured?

The internal energy of a real gas can be measured using a calorimeter, which is a device that measures the heat absorbed or released by a substance. The change in temperature of the gas is used to calculate its internal energy based on the specific heat capacity of the gas.

## 5. What is the significance of understanding the internal energy of a real gas?

Understanding the internal energy of a real gas is crucial in various fields, including thermodynamics, chemistry, and engineering. It helps us understand the behavior of gases under different conditions and how energy is transferred and transformed within the system. This knowledge is essential in designing and optimizing various processes and systems that involve real gases, such as refrigeration, combustion, and gas storage.

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