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

## Main Question or Discussion Point

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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Andrew Mason
Homework Helper
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

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.

I like Serena
Homework Helper
In general we have the equations for small changes dP, dV, dU, dH:
dU=dQ - PdV
dH=dQ + VdP

For 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.