Thermodynamics of a perfect liquid, help please

[kawf]

Homework Statement

Water, assumed to be a perfect liquid, has a density of 1000 kg/m3 and a specific heat of 4184 J/kgK. The water undergoes an adiabatic, frictionless process in which its pressure is raised from 200 kPa to 1500 kPa. Find:
1. change in temperature
2. change in specific internal energy
3. change in specific enthalpy
4. temperature change required for isobaric process to change the enthalpy that same amount as in part 3

Homework Equations

ds = c ln(P2/P1)
Tds = de
Tds = dh

The Attempt at a Solution

I have done the following, is this correct logic?

1. ds = c ln(P2/P1) = 4184 ln(1500/200) = 8430
Tds=cdT => dT = Tds/c = (298*8430)/4184 = 600K
so change in temp dT = 600K

2. Tds = de
de = 298 * 8430 = 2512 kJ/kg

3. Tds = dh
dh = 298 * 8430 = 2512 kJ/kg

4. I am not quite sure how to do this part.

Any help or suggestions are appreciated.

 

[anathema]

Thank you for sharing your solution.

Hello,

Your logic for parts 1-3 seems correct. For part 4, you can use the equation dH = CpdT, where Cp is the specific heat at constant pressure. Since the process is isobaric (constant pressure), you can assume that Cp remains constant. Thus, you can rearrange the equation to solve for dT as:

dT = dH/Cp

Since you already calculated dH in part 3, you can use that value and the specific heat of water (Cp = 4184 J/kgK) to calculate the required temperature change:

dT = (2512 kJ/kg)/(4184 J/kgK) = 0.6 K

Therefore, the required temperature change for an isobaric process to change the enthalpy by the same amount as in part 3 is 0.6 K.

Hope this helps! Let me know if you have any further questions.

 

[kerimek]

Thank you.

Your approach for the first three parts is correct. For the fourth part, you can use the formula for enthalpy change in an isobaric process, which is given by Δh = CpΔT, where Cp is the specific heat at constant pressure. You can equate this to the change in specific enthalpy obtained in part 3 and solve for ΔT. This will give you the temperature change required for the isobaric process to change the enthalpy by the same amount as in part 3. Hope this helps!