# (Thermodynamics) Why Do I Use U For Constant Volume and H For Constant Pressure

• cnoa
In summary, for an ideal gas, the change in internal energy (U) is equal to the exchanged heat (Q) for constant volume, and the change in enthalpy (H) is equal to the exchanged heat for constant pressure. These equations can be used to calculate H, Q, U, and W, depending on the given circumstances.

#### cnoa

Why Do I Use U For Constant Volume and H For Constant Pressure?

Also, which can be calculated H, Q, U, W?

cnoa said:
Why Do I Use U For Constant Volume and H For Constant Pressure?

Also, which can be calculated H, Q, U, W?
For an ideal gas:

$\Delta U = nC_v\Delta T$

$\Delta H = \Delta U + \Delta (PV) = nC_v\Delta T + nR\Delta T = nC_p\Delta T$

I am not sure what you mean by your last question. They can all be calculated if you have sufficient information.

AM

cnoa said:
Why Do I Use U For Constant Volume and H For Constant Pressure?

I can't tell you why you do that but if there is no non-volumetric work the change of U or H is equal to the exchanged heat if you do so.

In general we have the equations for small changes dP, dV, dU, dH:
dU=dQ - PdV
dH=dQ + VdPFor constant volume dV=0, so we can write the first as:
ΔU=ΔQ

For constant pressure dP=0, so we can write the second as:
ΔH=ΔQ

These are the quantities that we can actually measure.Depending on circumstances we can calculate each of H, Q, U, and W.

The symbols used for thermodynamic variables, such as U for internal energy and H for enthalpy, are based on historical conventions and mathematical notations. These symbols were chosen to represent specific properties in thermodynamics equations and help us understand the behavior of substances under different conditions.

The use of U for constant volume and H for constant pressure is due to the fact that these variables are related to specific types of processes. In a constant volume process, the volume of a system remains constant, but the pressure and temperature may change. In this case, internal energy, represented by U, is a more relevant variable to consider, as it reflects the amount of energy contained within the system.

On the other hand, in a constant pressure process, the pressure of a system remains constant, but the volume and temperature may change. In this case, enthalpy, represented by H, is a more useful variable as it takes into account the energy transferred to or from the system through heat at constant pressure.

To answer the second part of your question, all of the variables H, Q, U, and W can be calculated as they are all related to each other through the first law of thermodynamics, which states that the change in internal energy of a system is equal to the sum of heat transferred to or from the system and work done on or by the system. So, depending on the given conditions and known variables, any of these can be calculated using appropriate equations.

In summary, the use of U for constant volume and H for constant pressure is a convention based on the type of process being considered, and all of these variables can be calculated using the first law of thermodynamics.

## 1. Why is U used for constant volume and H used for constant pressure in thermodynamics?

In thermodynamics, U represents the internal energy of a system, which is defined as the total energy of all the particles in the system. For a constant volume process, the volume of the system remains constant, meaning that no work is done by or on the system. Therefore, the change in internal energy (ΔU) is equal to the heat added to or removed from the system (Q). This is why U is used for constant volume processes.

On the other hand, H represents the enthalpy of a system, which is defined as the total energy of the system plus the product of the pressure and volume. For a constant pressure process, the pressure of the system remains constant, meaning that work is done by or on the system. Therefore, the change in enthalpy (ΔH) is equal to the heat added to or removed from the system (Q) plus the work done by or on the system (W). This is why H is used for constant pressure processes.

## 2. Can U be used for constant pressure processes and H for constant volume processes?

Technically, yes, U can be used for constant pressure processes and H can be used for constant volume processes. However, this would require making additional calculations to account for the work done by or on the system. It is more common and convenient to use U for constant volume processes and H for constant pressure processes as it simplifies the calculations and provides a clearer understanding of the energy changes in the system.

## 3. What is the relationship between U and H in thermodynamics?

The relationship between U and H can be described by the equation H = U + PV, where P is the pressure and V is the volume of the system. This equation shows that H is equal to the internal energy of the system plus the product of the pressure and volume. This relationship is important in understanding the difference between U and H and when to use them in thermodynamic calculations.

## 4. Why is the use of U and H important in thermodynamics?

The use of U and H is important in thermodynamics because it helps in understanding the energy changes that occur in a system during a process. By using U and H for different types of processes, we can easily calculate the heat added to or removed from the system and understand the work done by or on the system. This information is essential in many engineering and scientific applications, such as designing engines and power plants.

## 5. Can other variables be used for constant volume and constant pressure processes instead of U and H?

Yes, other variables such as internal energy per unit mass (u) and enthalpy per unit mass (h) can also be used for constant volume and constant pressure processes in thermodynamics. However, using U and H is more common and convenient as they represent the total energy of the system and account for the effects of both heat and work on the system. Additionally, u and h are just specific forms of U and H, respectively, and can be derived from them using appropriate conversions.

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