# Constant volume Specific heat and internal energy relationship in nonideal gas.

• kntsy
In summary, the conversation discusses the relationship between internal energy (U), temperature (T), and volume (V) in both ideal and non-ideal gases. It is stated that in a non-ideal gas, the internal energy is solely dependent on temperature (U = C_VdT) while in an ideal gas, the change in volume also affects the internal energy (U = \left(\frac {\partial V}{\partial T}\right)_P \left(C_P-C_V\right) - P). This explains why \left(\frac {\partial U}{\partial V}\right)_T is equal to 0 in a non-ideal gas, but not in an ideal gas. The conversation ends with a request for further clarification
kntsy
Hi,
1.
$$\color{blue}dq=dU+PdV$$
so
$$C_V = \left(\frac {\partial q}{\partial T}\right)_V= \left(\frac {\partial U}{\partial T}\right)_V$$
$$dU=C_{V}dT$$
so
$$\color{red}\left(\frac {\partial U}{\partial V}\right)_T = 0$$
meaning that internal energy of NONideal gas is a sole function of T?
2.
As
$$\color{blue}dq=dU+PdV$$
so
$$\left(\frac {\partial U}{\partial V}\right)_T= \left(\frac {\partial V}{\partial T}\right)_P \left(C_P-C_V\right) - P$$
why? even for ideal gas the change in volume results in change in internal energy:
$$\color{red}\left(\frac {\partial U}{\partial V}\right)_T \not= 0??$$

Last edited:

## 1. What is constant volume specific heat?

Constant volume specific heat, also known as Cv, is the amount of heat required to raise the temperature of a unit mass of gas by 1 degree Celsius at constant volume.

## 2. How is constant volume specific heat different in nonideal gases?

In nonideal gases, the constant volume specific heat can vary depending on factors such as temperature, pressure, and composition. This is due to the fact that nonideal gases do not always follow the ideal gas law, which assumes that all gas particles have no volume and do not interact with each other.

## 3. What is the relationship between constant volume specific heat and internal energy in nonideal gases?

In nonideal gases, the internal energy is directly related to the constant volume specific heat. This means that as the internal energy of a gas increases, so does its constant volume specific heat. This relationship is important in understanding the behavior of nonideal gases.

## 4. How is the constant volume specific heat of a nonideal gas measured?

The constant volume specific heat of a nonideal gas can be measured experimentally using a bomb calorimeter. This device measures the change in temperature of a gas when a known amount of heat is added at constant volume. The resulting change in temperature can then be used to calculate the constant volume specific heat.

## 5. Why is the constant volume specific heat of nonideal gases important?

The constant volume specific heat of nonideal gases is important in various scientific and engineering applications. It helps in predicting the behavior of gases under different conditions, such as in combustion processes or in the design of gas-powered engines. It also allows for a better understanding of the thermodynamic properties of nonideal gases.

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