Thermodynamics Ch 17 – Heat and the 1^st Law of Thermodynamics
Heat and Internal Energy
Internal energy is all the energy of a system that is associated with its microscopic components – atoms and molecules – when viewed from a reference frame at rest with respect to the center of mass of the system. Heat is defined as the transfer of energy across the boundary of a system due to a temperature difference between the system and its surrounds.
Units of heat
calorie	the amount of energy transfer required to raise the temp of 1 gram of water from 14.5 °C to 15.5 °C
joule	The SI unit: 1 cal = 4.186 Joules 1 kcal = 1 Calorie = 4186 Joules
BTU	English unit: (Q required to raise 1 lb, 1 °F) 1 Btu = 1054 Joules
Specific Heat and Calorimetric
Heat Capacity, C : Q = C ΔT C, the heat capacity is defined as the energy needed to raise the temperature of a sample by 1°C								Specific Heat: Q = m c ΔT c, the heat capacity of a sample per unit mass
Question: Which would require more energy to bring to boil if both are initially at room temperature? A) A cup of water B) A swimming pool full of water Ans: I wouldn’t want to have to pay the energy bill required to raise a swimming pool full of water to its boiling point. Conclusion: The greater the mass…the more energy required to bring to boiling point.				Question: Which would require more energy to rise from 20 °C to 50 °C? A) A cup of water B) A cup of alcohol Ans: This one is harder…but I believe many know raising the temperature of alcohol requires less heat than water. Conclusion: The material being heater makes a bit difference, so materials like water require much more energy to change its temperature compared to materials like alcohol and sand.
Question: Which would require more energy to bring to boil? A) A cup of water at 20 °C B) A cup of water at 90 °C Ans: This one is easy…the one at 90 °C is almost at boil already, thus the energy input required to bring it to boil will way less than the cup at 20°C Conclusion: The greater the ΔT…the greater amount of energy was required.				Question: Which would require more energy to bring to 20 °C? C) A cup of ice at 0 °C D) A cup of water at 0 °C Ans: This one is easy…imagine adding 0°C water to your Coke or Pepsi to cool it down. 0°C ice requires much energy to bring it to 0°C water. Conclusion: The change of state requires a large change of energy. (This refers to section 12.8)
Demo: Heat Capacity: TH-B-HC
Latent Heat
SI units are generally preferable, but I’m presenting this section in cgs units Question: A large block of ice, 1000 g, is at -20 °C. How much energy is required to bring it to 100 °C steam? Ans: v à vaporization f à fusion units of c à calories / (gram C°) Q = cice m ΔT + m Lf + cwaterm ΔT + m Lv Q = ½ (1000)(20) + 1000(80) + 1 (1000)(100) + 1000 (539) Q = 10,000 cal + 80,000 cal + 100,000 cal + 539,000 cal Q = 729,000 calories (1 Calorie = 1 kilocalorie) Q = 729 Calories (4.186 J / Cal) Q = 3052 Joules (a good exercise for you is to work the problem out using SI units)
Demo: Latent Heat: TH-C-LH Demo: Drinking Duck: TH-C-DD
Work and Heat in Thermodynamics
Using a macroscopic approach, the state of the system is described using P, V, T, and internal energy, so these are called “state variables.”					“Transfer variables” only involve transfer of energy. So no “change” or transfer of energy…no transfer variables.
Work = force applied through a displacement Work = F ◦ dr Work = -F dy Work = -PA dy Work = -∫ P dV from Vi to Vf					The work done on a gas as it is taken from an initial state to a final state depends on the path between these states
Demo: Diffusion in Air: TH-D-DA
The 1^st Law of Thermodynamics
The 1^st law of thermodynamics (an energy conservation equation specifying that) the only type of energy that changes in the system are the internal energy, Eint.									ΔEint = Q + W Internal Energy is a state variable just like P, V, and T dEint = dQ + dW
thus Q + W is INDEPENDENT of path
An isolated system is a system that no energy is transferred by heat and the work done on the system is zero. (Doesn’t interact with environment) Q = W = ΔEint = 0 Joules ΔEint-i = ΔEint-f									Non-isolated, but is cyclic (starts and ends in the same state) ΔEint = 0 Joules Thus Q (energy added to system) is equal to the negative Work. Q = -Work
Demo: Fire Syringe: TH-B-FS
Some Apps of the 1^st Law of Thermodynamics
ΔEint = Q + W
An adiabatic process is one that no energy enters or leaves from the system by heat. Q = 0 Joules		ΔEint = Work As gas expands adiabatically the temperature reduces accordingly								For a cloud in deep space that is spurting out material very fast, at that point the temperature can go below the ambient background radiation temperature of 3 Kelvin
Isobaric (Constant Pressure) W = -P ΔV P is a constant			A plot of P vs V for an ideal gas yields a hyperbolic curve (an isotherm) Isothermic (constant Temp) ΔEint = 0 Joules Q = -W W = -∫ P dV W = -∫ (nRT/V) dV Work = -nRT ln(Vf/Vi) Work = nRT ln(Vi/Vf)							Isovolumetric ΔEint = Q If energy is added by heat to a system, all of the transferred energy remains in the system as increased internal energy
Energy-Transfer Mechanics
Conduction P = Q / t = kA dT/dx dx: The thicker the wall…more isolated A: More area…the more energy flows through the wall dT: The greater the temperature difference …the more energy flow through the wall k: And different materials will have different coefficients for heat flow P = kA ΔT/Δx P = A ΔT/(Δx/k) P = A ΔT/(ΣRi) R à ft^2 °F hr/Btu 1 ft^2 °F hr/Btu (0.305m/ft)^2 (5°C/9°F)(3600s/hr)(1Btu/1054J) = 0.1765 m^2°F sec / J R-11 english = R-2 in metric
Convection Energy transferred by the movement of a warm medium Demo:Convection Currents in Air: TH-B-CC
Radiation Stefan’s Law: P = σAeT^4 σ = 5.669 x 10-8 W/m^2K^4, e is emissivity (0 to 1) Ideal absorber, e = 1 (Black Body) Ideal reflector, e = 0 Demo: Light the Match: TH-B-LM