Thermodynamics, adiabatic process

In summary, the equation for internal energy can be written as U = (f/2)*p*V using the ideal gas law. When differentiating this equation, the values of p and V are those of the immediate states and can vary depending on the process. The values of p and V would need to be kept inside the integrand unless they are constant or a known function of other variables. In practice, the equation for internal energy is only expressed in this way if p or V are constant during the process.
  • #1
Niles
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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?

Thanks in advance.
 
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  • #2
I think you mean not delta but dU=(f/2)(Vdp+pdV). The values are those of the immediate states, and can vary depending on what you're doing to the gas. If you wanted to integrate dU to find the change in energy during a process, you would need to keep p and V inside the integrand unless they were constant, and this could make the integration complicated.

In practice, then, you wouldn't express dU this way unless p or V were constant (or a known function of other variables) during the process. For example, if you heat a gas while expanding from V1 to V2 in an isobaric process, then p is constant, dp=0, and U=(f/2)p(V2-V1).
 

Related to Thermodynamics, adiabatic process

What is thermodynamics?

Thermodynamics is the branch of physics that deals with the relationships between heat, work, energy, and temperature. It studies how these quantities change and interact with each other in various systems.

What is an adiabatic process?

An adiabatic process is a thermodynamic process in which there is no transfer of heat between the system and its surroundings. This means that the system is insulated and does not exchange energy in the form of heat with its surroundings.

What is the first law of thermodynamics?

The first law of thermodynamics, also known as the law of conservation of energy, states that energy cannot be created or destroyed, only transferred or converted from one form to another. In other words, the total energy within a closed system remains constant.

How is an adiabatic process different from an isothermal process?

An adiabatic process does not allow for the transfer of heat, whereas an isothermal process occurs at a constant temperature. This means that in an adiabatic process, the change in internal energy is equal to the work done on or by the system, while in an isothermal process, the change in internal energy is zero.

What are some real-life examples of adiabatic processes?

Some examples of adiabatic processes include the compression or expansion of a gas in a piston without heat exchange, the rapid expansion of air in a bicycle pump, and the compression of a gas in a diesel engine. The Earth's atmosphere also experiences adiabatic cooling as air rises and expands in areas of low pressure.

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