- #1
Saladsamurai
- 3,020
- 7
Here are some general questions regarding my current reading. I am looking in my text at 2 equations for specific energy and specific enthalpy:
[itex]u = u(T,v)\qquad(1)[/itex]
[itex]h = h(T,p)\qquad(2)[/itex]
Question 1: Are not the properties fixed by any 2 independent priorities? Why have we chosen to speak of u as u(T, v) in lieu of u(T, p) and the same for h ? Is it more convenient to out them in these terms for some reason?
Now, if we put (1) and (2) in differential form, we have:
[tex]du = \left(\frac{\partial{u}}{\partial{T}}\right)_v dT + \left(\frac{\partial{u}}{\partial{v}}\right)_T dv\qquad(3)[/tex]
[tex]dh = \left(\frac{\partial{h}}{\partial{T}}\right)_p dT + \left(\frac{\partial{h}}{\partial{p}}\right)_T dp\qquad(4)[/tex]
Question 2:
It says that for an ideal gas:
[tex]\left(\frac{\partial{u}}{\partial{v}}\right)_T \text{ and }\left(\frac{\partial{h}}{\partial{p}}\right)_T [/tex]
are equal to zero. Can someone clarify this? Is there some mathematical reasoning behind this? Or is this simply something that we have observed? Or both?
Question 3:
Going along with assumptions above (i.e., dh/dp = 0 and du/dv = 0) we can assert that for an ideal gas, specific energy and specific enthalpy are both functions of temperature alone, correct?
[itex]u = u(T,v)\qquad(1)[/itex]
[itex]h = h(T,p)\qquad(2)[/itex]
Question 1: Are not the properties fixed by any 2 independent priorities? Why have we chosen to speak of u as u(T, v) in lieu of u(T, p) and the same for h ? Is it more convenient to out them in these terms for some reason?
Now, if we put (1) and (2) in differential form, we have:
[tex]du = \left(\frac{\partial{u}}{\partial{T}}\right)_v dT + \left(\frac{\partial{u}}{\partial{v}}\right)_T dv\qquad(3)[/tex]
[tex]dh = \left(\frac{\partial{h}}{\partial{T}}\right)_p dT + \left(\frac{\partial{h}}{\partial{p}}\right)_T dp\qquad(4)[/tex]
Question 2:
It says that for an ideal gas:
[tex]\left(\frac{\partial{u}}{\partial{v}}\right)_T \text{ and }\left(\frac{\partial{h}}{\partial{p}}\right)_T [/tex]
are equal to zero. Can someone clarify this? Is there some mathematical reasoning behind this? Or is this simply something that we have observed? Or both?
Question 3:
Going along with assumptions above (i.e., dh/dp = 0 and du/dv = 0) we can assert that for an ideal gas, specific energy and specific enthalpy are both functions of temperature alone, correct?