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Thermodynamics-Properties

Introduction

This section includes notes on certain important thermodynamic properties including enthalpy (h), Specific heat (cv,cp), gas constant (R), and Entropy (S)

Enthalpy

In many thermodynamic fluid process analyses the sum of the internal energy (U) and the product of pressure (P) and volume(V) is present.  The combination (U + PV) is called the enthalpy of the fluid.   H is a thermodynamic fluid property but is does not have an absolute value(because it includes internal energy U )value and therefore enthalpy changes are generally applied or enthalpy values are identified relative to a fixed state e.g. water at 273 deg.K .  It is important to note that enthalpy is simply a combination of properties ..it is not a form of stored energy although for certain applications it can be treated as energy.

H = U + PV ..........(extensive property)

per unit mass

h = u + Pv ...........(intensive property)

When referring for water and steam and other fluids at different states in tables the following enthalpy designations are used

  • hg..specific enthalpy of saturated vapor
  • hf..specific enthalpy of saturated liquid
  • hi..specific enthalpy of saturated solid
  • hfg..specific latent heat of vaporisation = h g - h f
  • hif..specific latent heat of fusion = h f - h i
  • hig..specific heat of sublimation = h g - h i

Specific Heat Capacity

The heat capacity of a substance is classically defined as the amount of heat needed to raise unit mass of a substance one degree Centigrade.

In SI units the specific heat capacity is the amount of heat required to raise 1 kg mass through 1 degree kelvin. (Unit kJ/kg.K)

Note:The specific heat of a substance is the ratio of the heat capacity of a substance relative to a reference substance generally water.

The heat capacity of water is one calorie per degree C (classical) or (4180 J/kg.K )   The specific heat of a substance relative to water will be numerically equal to its heat capacity in classical units, but not in SI units ;

The term specific heat is often used when the heat capacity actually is meant.  This page is concerned only with heat capacity (to be called specific heat capacity). Because the heat capacities of most substances vary with changes in temperature, the temperatures of both the specified substance and the reference substance must be known in order to give a precise value for the specific heat.  

Specific Heat Capacities of Gases

Four specific heats are for gases are used.

  • Cv = Molar specific heat at constant volume.
  • Cp = Molar specific heat at constant pressure.
  • cv = Specific heat at constant volume.
  • cp = Specific heat at constant pressure.

Note: The molar specific heats are mainly used for chemical studies

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The specific heat varies with temperature and pressure.  The graph below this illustrates this characteristic for cp. for air
Tables below show the variation of cp and cp with temperatures...


Variation of cp (for Air) with temperature and pressure



Latent Heat

The latent heat of fusion is the amount of heat required to convert unit mass a substance from solid to liquid without change of temperature..

The latent heat of vaporisation is the amount of heat required to convert unit mass of a substance from liquid to vapour without change of temperature.


Gas Constant R

The gas constant R is derived from the equation of state

Pv = RT .. for unit mass of gas

PV = mRT

The gas constant R is different for each gas and has different units depending on the unit systems used. Typical units are (kJ/kg.K).

The universal gas constant Ru is the same for all gases and is defined by

PV = NRuT

  • R = Gas Constant = Ru /M
  • Ru = Universal Gas Constant
  • v = Gas volume (m3 )
  • V = Gas Volume (m3 )
  • N = Number of Moles
  • T = Absolute Temperature deg K
  • M = Molar mass (kg)
  • P = Absolute Pressure N/m3 (kg)




Table of Gas Properties for Various Gases

Based on a pressure of 1.032 bar and at 0oC

Gas cp cv cp / cv cp - cv
Acetylene 1.616 1.3 1.2431 0.316
Air 1.005 0.718 1.3997 0.287
Ammonia 2.056 1.568 1.3112 0.488
Argon 0.52 0.312 1.6667 0.208
Carbon Dioxide 0.816 0.627 1.3014 0.189
Carbon Disulphide 0.582 0.473 1.2304 0.109
Carbon Monoxide 1.038 0.741 1.4008 0.297
Chlorine 0.473 0.36 1.3139 0.113
Coal Gas 2.14 1.59 1.3459 0.55
Ethylene 1.47 1.173 1.2532 0.297
Helium 5.2 3.121 1.6661 2.079
Hydrochloric Acid 0.795 0.567 1.4021 0.228
Hydrogen 14.05 9.934 1.4143 4.116
Hydrogen Sulphide 0.992 0.748 1.3262 0.244
Krypron 0.25 0.151 1.6556 0.099
Methane 2.19 1.672 1.3098 0.518
Neon 1.03 0.618 1.6667 0.412
Nitrogen 1.038 0.741 1.4008 0.297
Oxygen 0.909 0.649 1.4006 0.26
Propane 1.549 1.36 1.1390 0.189
Sulphur Dioxide 0.586 0.456 1.2851 0.13
Water Vapor 1.842 1.381 1.3338 0.461
Xenon 0.16 0.097 1.6495 0.063


Zero Pressure - (pseudo ideal gas) Gas properties - Showing Temperature relationships

Air
Temperature cp cv cp / cv cp - cv
0 1.004 0.717 1.4003 0.287
50 1.006 0.719 1.3992 0.287
100 1.01 0.723 1.3970 0.287
150 1.016 0.729 1.3937 0.287
200 1.024 0.737 1.3894 0.287
400 1.068 0.781 1.3675 0.287
600 1.115 0.828 1.3466 0.287
800 1.154 0.867 1.3310 0.287
1000 1.185 0.898 1.3196 0.287
1500 1.235 0.948 1.3027 0.287
2000 1.266 0.978 1.2945 0.288
2500 1.287 1 1.287 0.287
Carbon Dioxide
Temperature cp cv cp / cv cp - cv
0 0.817 0.628 1.3010 0.189
50 0.869 0.68 1.2779 0.189
100 0.916 0.727 1.2600 0.189
150 0.958 0.769 1.2458 0.189
200 0.995 0.806 1.2345 0.189
400 1.113 0.924 1.2045 0.189
600 1.195 1.006 1.1880 0.189
800 1.253 1.064 1.1776 0.189
1000 1.294 1.105 1.1710 0.189
1500 1.354 1.165 1.1622 0.189
2000 1.387 1.198 1.1578 0.189
2500 1.407 1.218 1.1552 0.189
Carbon Monoxide
Temperature cp cv cp / cv cp - cv
0 1.04 0.743 1.3997 0.297
50 1.041 0.745 1.3973 0.296
100 1.045 0.748 1.3971 0.297
150 1.05 0.754 1.3926 0.296
200 1.074 0.777 1.3822 0.297
400 1.106 0.809 1.3671 0.297
600 1.157 0.86 1.3453 0.297
800 1.199 0.902 1.3293 0.297
1000 1.231 0.934 1.3180 0.297
1500 1.28 0.983 1.3021 0.297
2000 1.306 1.01 1.2931 0.296
2500 1.323 1.026 1.2895 0.297
Hydrogen
Temperature cp cv cp / cv cp - cv
0 14.19 10.07 1.4091 4.12
50 14.37 10.25 1.402 4.12
100 14.46 10.33 1.3998 4.13
150 14.49 10.37 1.3973 4.12
200 14.51 10.38 1.3979 4.13
400 14.59 10.46 1.3948 4.13
600 14.79 10.66 1.3874 4.13
800 15.12 10.99 1.3758 4.13
1000 15.53 11.41 1.3611 4.12
1500 16.58 12.46 1.3307 4.12
2000 17.45 13.33 1.3091 4.12
2500 18.12 14 1.2943 4.12
Nitrogen
Temperature cp cv cp / cv cp - cv
0 1.039 0.742 1.4003 0.297
50 1.04 0.743 1.3997 0.297
100 1.042 0.745 1.3987 0.297
150 1.046 0.749 1.3965 0.297
200 1.052 0.755 1.3934 0.297
400 1.091 0.795 1.3723 0.296
600 1.139 0.842 1.3527 0.297
800 1.181 0.885 1.3345 0.296
1000 1.215 0.918 1.3235 0.297
1500 1.269 0.972 1.3056 0.297
2000 1.298 1.001 1.2967 0.297
2500 1.316 1.019 1.2915 0.297
Oxygen
Temperature cp cv cp / cv cp - cv
0 0.915 0.655 1.3969 0.26
50 0.922 0.663 1.3906 0.259
100 0.934 0.674 1.3858 0.26
150 0.948 0.688 1.3779 0.26
200 0.963 0.703 1.3698 0.26
400 1.024 0.764 1.3403 0.26
600 1.069 0.809 1.3214 0.26
800 1.1 0.84 1.3095 0.26
1000 1.122 0.863 1.3001 0.259
1500 1.164 0.904 1.2876 0.26
2000 1.2 0.94 1.2766 0.26
2500 1.234 0.975 1.2656 0.259
Steam Properties Links
  1. Thermodynamics..NASA - Glenn Research center at Series of informative notes on Thermodynamics
  2. Thermodynaic properties,property relationships and processes..A very detailed clear study of the subject, 3,3 Mbyte download

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Last Updated 27/01/2013