Mech 261 – Thermo I Week 2 Notes: Parts of Chapter 4 (Pure Substances)

Chapter 4: Properties of Pure Substance [text pg. 104] A substance that has a fixed chemical composition throughout is called a pure substance. Water, nitrogen, helium and carbon dioxide, for example, are all pure substance. Phases of a Pure Substance [text pg. 104] You guessed it. There are 3 phases: Gas, Liquid and Solid. Compressed Liquid and Saturated Liquid [text pg. 106]

Compressed liquid or sub-cooled liquid = a liquid that is not about to vaporize. Saturated liquid = a liquid that is about to vaporize. Saturated vapour = a vapour that is about to condense. Superheated vapour = a vapour that is not about to condense. Saturation Temperature = at a given pressure, the temperature at which a pure substance changes phase. Saturation Pressure = at a given temperature, pressure at which a pure substance changes phase. Latent Heat = the amount energy absorbed or release during a phase-change. Latent Heat of Fusion = the amount of energy released during freezing. Latent Heat of Vaporization = the amount of energy absorbed during vaporization.

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Property Diagrams for Phase-Change Processes [text pg. 110]

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Property Tables [text pg. 116] At the back of the text there are tables detailing the properties of a variety of important thermodynamic materials.

Enthalpy – A Combined Property [text pg. 116] Enthalpy, h is an energy property of thermodynamic substances. It is a combination of pressure and temperature.

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Saturated Liquid and Saturated Vapor States [text pg. 117]

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The Ideal-Gas Equation of State [text pg. 126] Equation of State = any equation that relates the pressure, temperature and specific volume of a substance. Gas = Vapour (Vapour implies the gas is not far from the state of condensation). Ideal Gas Equation of State = the simplest and best known equation of state.

These equation are magic! They are very useful and common. Several things …

• R is a gas CONSTANT that is specific to a substance (it is not universal). • This second form (eq. 4-13) is by far the most used as it contains a mass term. • The first form (eq. 4-10) is useful if need or have the materials specific volume or density.

Some variables and units …

P = Pressure N/m2, Pa V = Volume, m3 ν or = specific volume, m3/kg ρ = density, kg/m3 (note: ρ = m/V = 1/ν) R = gas constant, kJ/kg·K T = Temperature, K Also … RU = Universal gas constant, units variable … see table below. N = mole number or number of moles of substance. M = molar mass or molecular weight, units variable

(mass of one mole of a substance. Gram-mole or gmole Kilogram-mole or kgmole, Pound-mole or lbmol or lbm)

For example … Nitrogen’s molecular weight is 14 (from the periodic table of elements). If we have 1 mole of N2 we have 2x14 = 28 grams of N2. Also if we have 1 kmol we have 1 kg of N2. That is, M = 28 kg/kmol or 28 lbm/lbmol of N2.

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Take note …

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Note that the air density in the tire can be calculated in both the cooler case and the warmer case using: Pν = RT

Recall that ν = specific volume, m3/kg. So density, ρ = 1/ν, kg/m3. So

ν = RT/P or ρ = P/RT In Case 1 (25⁰C): ρ = 305x103 Pa / (0.287x103 J/kg·K x (25⁰C + 273K)) = 3.57 kg/m3 In Case 2 (34.8⁰C): ρ = 315x103 Pa / (0.287x103 J/kg·K x (34.8⁰C + 273K)) = 3.57 kg/m3 (same V = Const.) Ok, if the volume stays so constant … what is the volume? If we knew the mass of air in the tire, m we could work that out using:

PV = mRT -> Volume = V = mRT/P As we don’t know the mass of air, we can not work out the volume. In the same way, to work out the Volume, we would need the mass.

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