Thermodynamics - Enthalpy, internal energy, pv work, saturated liquid, vapor, quality

Enthalpy
- a thermodynamic function of a system, equivalent to the sum of the internal energy of the system plus the product of its volume multiplied by the pressure exerted on it by its surroundings.

- is the amount of energy in a system capable of doing mechanical work.


H = U + PV

H = m * Cp * dT

dH = dU + pdV + VdP

h = hf + (x)hfg

hfg = hg - hf


where:

H = enthalpy

U = internal energy

P = pressure

V = volume

m = mass

Cp = specific heat at constant pressure

dT = change in temperature

hf = specific enthalpy of saturated liquid

hg = specific enthalpy of saturated vapor

hfg = difference, hg - hf

x = quality



1. A steam turbine receives steam at a temperature of 500 C and pressure of 70 bar. If it expands isentropically to 0.1 bar, find the enthalpy after expansion.
find:

h2 = enthalpy after expansion


given:

at p1 = 70 bar and t1 = 500 C

we get from steam tables

h1 = 3410 KJ/kg

s1 = 6.796 KJ/kg K


at s1 = s2 (constant entropy) and 0.1 bar

sf = 0.649

sfg = 7.5


solving for x

s2 = sf + (x)sfg

6.796 = 0.649 + (x)7.5

x = 0.8196


now solve for h2

h2 = hf + (x)hfg

h2 = 192 + (0.8196)(2392)

h2 = 2152.2 KJ/kg



2. One pound of Water at 60°F is heated until it boils to 212 F. Calculate the change in enthalpy.
find:

dH = change in enthalpy


given:

m = 1 lb

t1 = 60 F

t2 = 212 F

Cp of water = 1 Btu/lb F


solution:

dH = m * Cp * dT

dH = 1 * 1 * (212 - 60)

dH = 152 Btu