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

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Discussion Overview

The discussion revolves around the use of internal energy (U) at constant volume and enthalpy (H) at constant pressure in thermodynamics. Participants explore the relationships between these quantities and their calculations, particularly in the context of ideal gases.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant states that for an ideal gas, the change in internal energy (ΔU) can be expressed as ΔU = nC_vΔT, while the change in enthalpy (ΔH) can be expressed as ΔH = nC_pΔT, indicating a relationship between these quantities and temperature changes.
  • Another participant mentions that the change in U or H is equal to the exchanged heat if there is no non-volumetric work involved, though they do not provide a rationale for why U is used for constant volume and H for constant pressure.
  • A further contribution outlines the differential forms of the equations for changes in internal energy and enthalpy, stating that at constant volume (dV=0), ΔU equals ΔQ, and at constant pressure (dP=0), ΔH equals ΔQ, emphasizing the measurable nature of these quantities.
  • Participants agree that H, Q, U, and W can all be calculated if sufficient information is available, but the specifics of these calculations are not fully resolved.

Areas of Agreement / Disagreement

Participants express various viewpoints on the relationships between U, H, Q, and W, but there is no consensus on the rationale for using U for constant volume and H for constant pressure. The discussion remains unresolved regarding the underlying reasons for these conventions.

Contextual Notes

Some assumptions regarding the conditions under which these equations apply may be implicit, and the discussion does not clarify all mathematical steps or dependencies on specific definitions.

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

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

[itex]\Delta U = nC_v\Delta T[/itex]

[itex]\Delta H = \Delta U + \Delta (PV) = nC_v\Delta T + nR\Delta T = nC_p\Delta T[/itex]

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.
 

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