Specific heat at constant pressure formula help

[yecko]

Homework Statement

https://i.imgur.com/f2vSXtq.png

Homework Equations

https://i.imgur.com/Kjy1Tzh.png

The Attempt at a Solution

In this question, the pressure is different at different point, in other words it is not constant throughout the system. Why the solution use c(p) (or "enthalpy" h which specified for constant pressure system) as part of the formula used?

Thank you very much!

 

[Chestermiller]

Homework Statement

View attachment 211514
https://i.imgur.com/f2vSXtq.png

Homework Equations

View attachment 211515
https://i.imgur.com/Kjy1Tzh.png

The Attempt at a Solution

In this question, the pressure is different at different point, in other words it is not constant throughout the system. Why the solution use c(p) (or "enthalpy" h which specified for constant pressure system) as part of the formula used?

Thank you very much!

For an ideal gas, enthalpy is independent of pressure. Doesn't the open system version of the first law require you to use enthalpy?

 

[yecko]

For an ideal gas, enthalpy is independent of pressure. Doesn't the open system version of the first law require you to use enthalpy?

Is that imply enthalpy is used just because the first law of thermodynamics is applicable?
And using Cp is not contradict to the situation of pressure changed, but rather Cp is used because it can trace out the enthalpy?
Thank you very much!

 

[Chestermiller]

Is that imply enthalpy is used just because the first law of thermodynamics is applicable?

Yes. The open system version of the first law tells us that, for your problem the change in enthalpy is equal to the change in kinetic energy.

And using Cp is not contradict to the situation of pressure changed, but rather Cp is used because it can trace out the enthalpy?
Thank you very much!

Yes.