# Internal energy, thermodynamics

• Niles
In summary, the equation for internal energy can be written as U = (f/2) * N * k * T or U = (f/2) * p * V. Differentiating this equation results in delta U = (f/2) * (delta_p * V + p * delta_V). V and p are not the initial or final values, but rather what they were before differentiating the expression. This can be further discussed in the "Advanced Physics" forum.
Niles
[SOLVED] Internal energy, thermodynamics

## Homework Statement

I have the equation for the internal energy:

U = (f/2) * N * k * T, where f is the degrees of freedom, N is the number of molecules, k is Bolzmann's constant and T is the temperature in Kelvin.

This can be written as U = (f/2)*p*V using the ideal gas law. Differentiating this I get:

delta U = (f/2)*(delta_p*V + p*delta_V).

In this equation, I know what delta_p and delta_V are, but what about V and p? Are they the initial or final states?

V and P are just what they were before you differentiated the expression.

you get delta_U as a function of P, V, Delta_p and delta_U. V and p are NOT the initial or final values.

I'm sorry, but I don't understand what you mean.

V and p are not the final or initial values? If not, what are they then?

## 1. What is internal energy?

Internal energy is the total potential and kinetic energy contained in a system, including the energy of the particles that make up the system.

## 2. How is internal energy related to thermodynamics?

Internal energy is a key concept in thermodynamics, as it represents the total energy of a system that can be converted into work. It is used to calculate changes in temperature, pressure, and volume in thermodynamic processes.

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

The internal energy of a system is affected by several factors, including the number of particles in the system, the temperature of the system, and the amount of heat and work that is added or removed from the system.

## 4. What is the first law of thermodynamics?

The first law of thermodynamics states that energy cannot be created or destroyed, but it can be transferred from one form to another. This means that in any thermodynamic process, the total energy of the system and its surroundings remains constant.

## 5. How is internal energy measured?

Internal energy is typically measured in joules (J) or calories (cal). In scientific experiments, it is often measured indirectly by measuring changes in temperature, pressure, and volume, and then using the first law of thermodynamics to calculate the change in internal energy.

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