Why is enthelpy a function of Temperature and Pressure?

In summary, the conversation discusses the equations dU = dw + dq and H = U + pV, and questions why enthalpy is a function of temperature and pressure. The concept of enthalpy being a function of p and T is explained through the equation dH = (delta H/delta T)dT + (delta H/delta p)dp. The conversation also suggests an alternative equation, dH = (delta H/delta T)dT + (delta H/delta V)dV, which is not used due to the definition of U in the total differential of the heat function.
  • #1
tkdiscoverer
2
0
right now, I'm following the MIT thermodynamics video lecture.

I've gone thru

dU = [STRIKE]d[/STRIKE]w + [STRIKE]d[/STRIKE]q
([STRIKE]d[/STRIKE] for "is path dependent")

and

H = U + pV

But why is enthalpy a function of temperature and pressure?
is it because pV = nRT and thus, V = nRT/p, so we only need p and T to get V?

dH = ( [itex]\delta[/itex] H/ [itex]\delta[/itex] )TdT + ( [itex]\delta[/itex] H/ [itex]\delta[/itex] p)dp

but why not:
dH = ([itex]\delta[/itex]H/[itex]\delta[/itex] T)dT + ([itex]\delta[/itex]H/[itex]\delta[/itex]V)dV ?

Thanks! : D
 
Last edited:
Science news on Phys.org
  • #2
You have (I won't write the path-dependent parts explicitly; just assume they are there :D ):
[tex]
\mathrm{d}E = T\mathrm{d}S - P\mathrm{d}V
[/tex]

We know that [itex]\mathrm{d}Q = T\mathrm{d}T[/itex], so that for a process at constant pressure we can rewrite the quantity of heat as the differential:
[tex]
\mathrm{d}Q = \mathrm{d}E + P\mathrm{d}V = \mathrm{d}(E + PV) = \mathrm{d}W
[/tex]

of some quantity
[tex]W = E+PV[/tex]

If you now want to find the total differential of the heat function itself (now no longer assuming constant pressure), you can easily get:
[tex]
\mathrm{d}W = T\mathrm{d}S + V\mathrm{d}P
[/tex]

For your notation: look at the definition of your [itex]U[/itex]. When you make the total differential of the heat function, you have to write explicitly the terms for the energy, where [itex]-P\mathrm{d}V[/itex] cancels with one of the differential you get from [itex]\mathrm{d}(PV)[/itex] in the heat function.
 
Last edited:

1. Why does enthalpy change with temperature?

Enthalpy is a measure of the total energy of a system, including its internal energy and the work it can do. As temperature increases, the internal energy of a system also increases, resulting in a higher enthalpy.

2. How does pressure affect enthalpy?

Pressure is a measure of the force exerted on a system. As pressure increases, the volume of a gas decreases, leading to a decrease in enthalpy. This is because the gas molecules are closer together and have less room to move, resulting in a decrease in the system's internal energy.

3. Why is enthalpy a state function?

Enthalpy is considered a state function because it only depends on the current state of the system, not the path taken to reach that state. This means that the enthalpy of a system will be the same regardless of how the system reached that particular state.

4. How does temperature and pressure affect the enthalpy of a reaction?

In a chemical reaction, the enthalpy change is determined by the difference in enthalpy between the products and reactants. Temperature and pressure can affect this enthalpy difference, as they can change the internal energy and work done by the system, ultimately affecting the overall enthalpy change of the reaction.

5. What is the relationship between enthalpy and heat?

Enthalpy and heat are closely related, as enthalpy is defined as the heat content of a system at a constant pressure. This means that the change in enthalpy of a system is equal to the heat added or released during a process at constant pressure.

Similar threads

Replies
11
Views
165
Replies
31
Views
1K
Replies
1
Views
535
Replies
13
Views
1K
Replies
14
Views
1K
  • Thermodynamics
Replies
4
Views
1K
Replies
3
Views
958
  • Thermodynamics
Replies
20
Views
1K
Replies
3
Views
2K
Back
Top