# Thermodynamics Properties

### Thermodynamics Properties Notes

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