First Law of Thermodynamics

• First law of thermodynamics prepared by Engr. Charles Fausto

Heat Quantities

• Thermal energy is the random kinetic energy of particles in a system.
• Heat is thermal energy in transit due to a temperature difference.
• The SI unit for heat is the joule (J).
• Other units for heat: calorie (1 cal = 4.184 J) and British thermal unit (1 Btu = 1054 J).
• A "Calorie" used by nutritionists is a kilocalorie (1 Cal = 1 kcal = 10^3 cal).
• Specific heat (c) is the heat required to change the temperature of a unit mass of a substance by one degree.

Specific Heat Equation

• If a quantity of heat ΔQ is required to produce a temperature change ΔT in a mass m, then c = ΔQ / (mΔT) or ΔQ = cmΔT.
• In SI units, specific heat is measured in J/kg.K, equivalent to J/kg.°C
• The unit cal/g.°C is also used, where 1 cal/g.°C = 4184 J/kg.°C
• Water has c = 4180 J/kg.°C = 1.00 cal/g.°C
• The heat gained or lost by a body during a temperature change ΔT is given by ΔQ = mcΔT.
• The heat of vaporization (Lv) is the heat needed to vaporize a unit mass of liquid at a constant temperature.
• Water at 100°C has Lv ≈ 2.26 MJ/kg or 540 cal/g.
• The heat of sublimation is the heat to convert a unit mass of a substance from solid to gaseous state.
• Calorimetry problems involve thermal energy sharing and energy conservation in hot and cold objects with the equation: Sum of heat changes for all objects = 0.
• Heat outflow from a high-temperature system (ΔQout < 0) numerically equals the heat flowing into the low-temperature system (ΔQin > 0), assuming no energy loss in the system.

Absolute Humidity

• Absolute humidity is the mass of water vapor per unit volume of gas, typically in kg/m³ or g/cm³.
• Relative humidity (R.H.) is the ratio of water vapor mass per unit volume in air to the mass per unit volume in saturated air at the same temperature, often expressed as a percentage.
• Dew point is the temperature at which air becomes saturated upon cooling.
• Specifically, when air is cooled, it eventually reaches a temperature at which it is saturated; this temperature is the dew point. Below this temperature, water condenses.

First Law of Thermodynamics

• Heat (ΔQ) is thermal energy flowing due to temperature differences, flowing from hot to cold.
• Thermal equilibrium between two objects requires them to be in contact and also have the same temperature (i.e. no net heat transfer).
• If two objects are each in thermal equilibrium with a third, they're in thermal equilibrium with each other. This is the Zeroth Law of Thermodynamics.
• Internal energy (U) of a system is its total energy content, summing all forms of energy by atoms and molecules.
• Work done by a system (ΔW) is positive if the system loses energy. If the surroundings do work on the system, ΔW is negative.
• Small expansion ΔV of a fluid at constant pressure P results in work ΔW = PΔV.

The First Law of Thermodynamics

• The First Law of Thermodynamics, a conservation of energy statement, says that if heat ΔQ flows into a system, it appears as an increase in internal energy ΔU and/or work ΔW. The formula is ΔQ = ΔU + ΔW.
• An isobaric process occurs at constant pressure.
• An isovolumic process occurs at constant volume, with ΔW = PΔV = 0
• For the isovolumic process, the First Law of Thermodynamics becomes ΔQ = ΔU
• An isothermal process is a constant-temperature process.

Isothermal Change

• In an ideal gas during an isothermal process where atoms don't interact, ΔU = 0
• For an ideal gas in an isothermal change, ΔQ = ΔW.
• For an ideal gas changing isothermally from (P1, V1) to (P2, V2) where P1V1 = P2V2,
• ΔQ = ΔW = P₁V₁ln(V₂/V₁) = 2.30P₁V₁log(V₂/V₁)
• Here, ln and log are logarithms to the base e and base 10, respectively.
• An adiabatic process involves no heat transfer (ΔQ = 0). The first law becomes 0 = ΔU + ΔW.
• Work done by the system is at the expense of internal energy and vice versa.

Adiabatic Process

• For an ideal gas changing from conditions (P1, V1, T1) to (P2, V2, T2) in an adiabatic process:
• P1V1^γ = P2V2^γ and T1V1^(γ-1) = T2V2^(γ-1)
• Here, γ = cp/cv
• When a gas is heated at constant volume, the heat goes to increase the internal energy of the gas molecules.
• When a gas is heated at constant pressure, heat increases the internal energy and does mechanical work expanding the gas against constant pressure.
• Constant-pressure specific heat cp is greater than constant-volume specific heat cv.
• For an ideal gas of molecular mass M: cp - cv = R/M
• R is the universal gas constant.
• In SI (R = 8314 J/kmol·K, M in kg/kmol), cp and cv are in J/kg·K = J/kg·°C
• R is approximately 1.98 cal/mol·°C and M in g/mol, which means cp and cv are in cal/g·°C.
• Specific heat ratio (γ = cp/cv) is greater than unity for a gas. Kinetic theory indicates that for monatomic gases (He, Ne, Ar), γ = 1.67. For diatomic gases (O2, N2), γ = 1.40 at ordinary temperatures.

Pressure-Volume Diagrams

• Work is related to the area in a P-V diagram.
• The work done by a fluid during expansion is equal to the area beneath the expansion curve on a P-V diagram.
• In a cyclic process, the work output per cycle equals the area enclosed by the P-V diagram.
• Efficiency of a heat engine is defined as: eff = work output / heat input
• The Carnot cycle is the most efficient cycle possible.
• For a Carnot cycle operating between hot (Th) and cold reservoirs (Tc): effmax = 1 - (Tc/Th)
• Kelvin temperatures must be used in this equation.