Thursday, October 25, 2012

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
 

Sunday, October 21, 2012

THERMODYNAMICS - First law of thermodynamics, conservation of energy, internal energy

First law of thermodynamics

- conservation of energy

- energy can be transformed or changed from one form to another

- energy can neither be created nor destroyed

- the increase in the internal energy of a system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the work done by the system on its surroundings


dU = dQ - dW


dU = dQ - PdV


dU = TdS - PdV



where:

dQ = TdS

dW = PdV

dU = change in the internal energy of the system

dQ = heat added to the system

dW = work done by the system


sign convention of dQ and dW

(-) dQ < 0 if energy is lost from the system as heat

(+) dW > 0 if energy is lost from the system as work



1. Problem:

A cup of water (approx. 250 ml) is heated from 25 to 100 C. Find the change in internal energy for the cup of water?



find:

dU = change in internal energy of the cup of water


given:

V = 250 mL ---> a cup of water

t1 = 25 C

t2 = 100 C ---> boiling point of water


Solution:

Cp of water = 4.2 J/g C

Density of water = 1 g/mL


m = D * V

m = 1 g/ml * 250 ml

m = 250 g


dU = m * Cp * dT

dU = 250 * 4.2 * (100 - 25)

dU = 250 * 4.2 * 75

dU = 78,750 J or 78.75 kJ


Thus, to boil a cup of water,

it requires approximately

80 kJ

Monday, October 15, 2012

Thermodynamic Processes



Adiabatic process

- deflating a tire by releasing a valve and the valve stem will become quite cold during the process
- perfectly insulated containers
- thermally insulated wall
- sound propagation
- compressions and rarefactions of a sound wave
- adiabatic expansion of gas
- Hot air near the ground rises to the region of higher altitude,
where the pressure is lower, and expands. The process is adiabatic because
air is a poor heat conductor.
- events inside an engine cylinder are nearly adiabatic because the wide fluctuations in temperature take place rapidly
- fluid flow through a nozzle is fast and very little heat exchange between fluid and nozzle


isentropic process

An adiabatic process that is reversible

- air inside the tire expanding adiabatically
- rapid depressurization of gas in a cylinder

isenthalpic process

an adiabatic process that is irreversible and extracts no work

- Helium expanding across a valve in which the helium generally will increase in temperature
- air expanding across a valve
- throttling process: an ideal gas flowing through a valve in midposition
- viscous drag


Polytropic Process

a reversible process in which there is heat transfer

plot of the Log P (pressure) vs. Log V (volume) is a straight line.

Or stated in equation form PVn  = a constant.  


- expansion of the combustion gasses in the cylinder of a water-cooled reciprocating engine
- vapors and perfect gases in many non-flow processes


Steady flow

Fluid flow in which all the conditions at any one point are constant with respect to time.
Fluid flow without any change in composition or phase equilibria
 flow velocities do not vary with time

- groundwater and channel flows
- turbine   
- fluid heater
- orifice(throttling)
- nozzle


Non flow


- Heating at constant volume

- Adiabatic expansion in a cylinder

- Free Expansion (Joules experiment - valve is initially closed and then opened to equalize pressures)

- Heating a fluid in a cylinder at constant pressure


===========================

Important thermodynamic processes

===========================


Isobaric process

An isobaric process is a thermodynamic process in which the pressure remains constant

From the Greek isos, "equal," and barus, "heavy"


Examples of isobaric process

- movable piston in a cylinder

- boiler superheater, as the heat of the exiting steam is increased



Isochoric process

An isochoric process is a process during which volume remains constant.

From the Greek isos, "equal", and khora, "place."

An isochoric process is also known as an isometric process or an isovolumetric process.


Examples of Isochoric process

- heating air in closed tin can

- instantaneous burning of the gasoline-air mixture in an internal combustion engine

- heating a gas inside a rigid, closed box



Isothermal process

Isothermal process is a thermodynamic process in which the temperature remains constant

From the Greek words isos meaning "equal" and therme meaning. "heat" or thermos meaning "hot."


Examples of isothermal process

- system immersed in a large constant-temperature bath

- most reactions of an acid and base mixed together to form a salt

- melting and boiling

- living cell processes

- cycles of some heat engines

- sealed syringe




Adiabatic process

An adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid.

From Greek adiabatos, impassable: a-, not; diabatos, passable


Examples of adiabatic process

- deflating a tire by releasing a valve and the valve stem will become quite cold during the process

- perfectly insulated containers

- thermally insulated wall

- sound propagation

- compressions and rarefactions of a sound wave

- adiabatic expansion of gas

- Hot air near the ground rises to the region of higher altitude,
where the pressure is lower, and expands. The process is adiabatic because
air is a poor heat conductor.

- events inside an engine cylinder are nearly adiabatic because the wide fluctuations in temperature take place rapidly

- fluid flow through a nozzle is fast and very little heat exchange between fluid and nozzle



Isentropic process

An isentropic process is one during which the entropy of working fluid remains constant. In other words there is no heat transfer with the surroudings, and no change in entropy.

An adiabatic process that is reversible

From Greek word "iso" -same and "entropia" -a turning towards (disorder)


Examples of isentropic process

- air inside the tire expanding adiabatically
- rapid depressurization of gas in a cylinder




Isenthalpic process

An isenthalpic process or isoenthalpic process is a process that proceeds without any change in enthalpy

The process will be isenthalpic if there is no transfer of heat to or from the surroundings, no work done on or by the surroundings, and no change in the kinetic energy of the fluid.

An adiabatic process that is irreversible and extracts no work

From en-, meaning "to put into" and the Greek word -thalpein, meaning "to heat"


Examples of isenthalpic process

- Helium expanding across a valve in which the helium generally will increase in temperature

- air expanding across a valve

- throttling process: an ideal gas flowing through a valve in midposition

- throttling process: the lifting of a relief valve or safety valve on a pressure vessel (the specific enthalpy of the fluid inside the pressure vessel is the same as the specific enthalpy of the fluid as it escapes from the valve)

- viscous drag




Polytropic Process

A reversible process in which there is heat transfer

The plot of the Log P (pressure) vs. Log V (volume) is a straight line

PV^n  = constant

From Greek poly = many, -tropic = bend, curve, turn

  
Examples of polytropic process

- expansion of the combustion gasses in the cylinder of a water-cooled reciprocating engine

- vapors and perfect gases in many non-flow processes

- Compression or Expansion of a Gas in a Real System such as a Turbine



Steady flow process

Fluid flow in which all the conditions at any one point are constant with respect to time

Fluid flow without any change in composition or phase equilibria

Flow velocities do not vary with time


Examples of steady flow process

- groundwater and channel flows

- turbine   

- fluid heater

- orifice(throttling)

- nozzle



Non flow process

A thermodynamic process involving no fluid flow


Examples of non-flow process

- Heating at constant volume

- Adiabatic expansion in a cylinder

- Free Expansion (Joules experiment - valve is initially closed and then opened to equalize pressures)

- Heating a fluid in a cylinder at constant pressure