Physics 1710—Warm-up Quiz In Antarctica the thermometer reads –20 C; what is this temperature on a Fahrenheit thermometer? A.-36 o F B.-11 o F C.-4 o F D.-43 o F E.-20 o F

Physics 1710 C hapter 20 Heat & 1 st Law of Thermo Solution: o F = (180 o F/100 o C) o C +32 o F o F = (180 o F/100 o C) o C +32 o F =(1.8 o F/ o C)(-20 o C) +32 o F =(1.8 o F/ o C)(-20 o C) +32 o F = ( ) o F = -4 o F

No Talking! Think! Confer! Peer Instruction Time Physics 1710 C hapter 20 Heat & 1 st Law of Thermo What will happen to a heated ring? The hole will (1) get larger; (2) get smaller; (3) stay the same.

What will happen to a heated ring? The hole will Physics 1710 — e-Quiz Answer Now ! 1.Get larger 2.Get smaller 3.Stay the same

Time for Real Physics! Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Why did it happen? Physics 1710 C hapter 20 Heat & 1 st Law of Thermo ΔL = α LΔT ΔL

Physics 1710 Chapter 19 Temperature Ideal Gas Law Idealizations: Idealizations: no interaction between atoms no volume occupied by atoms Number of atoms n = m/M, Number of atoms n = m/M, m = mass; M = molar mass PV = n R T PV = n R T R = J/ mol K = L‧atm/mol K = L‧atm/mol K = 22.4 L‧atm / mol K = 22.4 L‧atm / mol K

Physics 1710 Chapter 19 Temperature Boltzmann’ Constant k = R/N A k = R/N A k = 1.38 x J/K = 1 yJ/ 7.25 K k = 1.38 x J/K = 1 yJ/ 7.25 K = 1 eV / 11,600 K = 1 eV / 11,600 K PV = N kT

Physics 1710 Chapter 19 Temperature Summary: Temperature is a measure of the average kinetic energy of a system of particles.Temperature is a measure of the average kinetic energy of a system of particles. Thermal Equilibrium means that two bodies are at the same temperature. Thermal Equilibrium means that two bodies are at the same temperature. The “Zeroth Law of Thermodynamics” states that if system A and B are n thermal equilibrium with system C, then A and B are in thermal Equilibrium with each other. The “Zeroth Law of Thermodynamics” states that if system A and B are n thermal equilibrium with system C, then A and B are in thermal Equilibrium with each other.

Physics 1710 Chapter 19 Temperature Kelvin is a unit of temperature where one degree K is 1/ of the temperature of the triple point of water (near freezing).Kelvin is a unit of temperature where one degree K is 1/ of the temperature of the triple point of water (near freezing). T C = (100/180) (T F – 32 ⁰F) T F = (180/100) T C + 32 ⁰F ∆L/L = α∆T ∆L/L = α∆T PV = n R T = N kT PV = n R T = N kT

1′ Lecture: The internal energy is the total average energy of the atoms of an object, average kinetic plus average potential. The internal energy is the total average energy of the atoms of an object, average kinetic plus average potential. Heat is the change in internal energy. Heat is the change in internal energy. The change in temperature is proportional to the change in internal energy (heat flow) when there is no change of phase and the system does no work. The change in temperature is proportional to the change in internal energy (heat flow) when there is no change of phase and the system does no work. The first law of thermodynamics states The first law of thermodynamics states ∆E = ∆Q - W Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

1′ Lecture: Conduction is the flow of kinetic energy from atom to atom. Conduction is the flow of kinetic energy from atom to atom. Convection is the transport of energy by bulk motion of atoms.Convection is the transport of energy by bulk motion of atoms. Radiation is the transfer of energy by electromagnetic waves. Radiation is the transfer of energy by electromagnetic waves. Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Heat Heat is the macroscopic manifestation of microscopic internal energy. Heat is the macroscopic manifestation of microscopic internal energy. Heat ∆Q in calories (or BTU) Heat ∆Q in calories (or BTU) 1 calorie (cal) is the amount of energy required to raise the temperature of kg of water from 14.5 C to 15.5 C (∆T = 1.00 C). 1 BTU is the heat to raise 1 Lb by 1 ⁰F. James Prescott Joule ( ) showed James Prescott Joule ( ) showed 1 calorie of heat = Joule 1 J = 1 N‧m Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

1 Calorie = 1000 calorie = 1 kcal Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Heat Capacity ∆Q = C ∆T C ≡ dQ/dT Specific Heat c = C /m C ≡ (1/m)dQ/dT ∆Q = (mc)∆T Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

How much heat is required to raise the temperature of 1 kg of water (1 liter) from 20 C to 100 C? Recall c = 1.00 kcal/kgC? Physics 1710 — e-Quiz Answer Now ! kcal 2.20 kcal 3.80 kcal kcal 5.None of the above.

Guided practice: ∆Q = (mc)∆T How much heat is required to raise the temperature of 1 kg of water (1 liter) from 20 C to 100 C? Recall c = 1.00 kcal/kgC? ∆Q = (mc)∆T ∆Q = (1.00 kg)(1.00 kcal/kg C) (100. C- 20. C) ∆Q = (1.00 kg)(1.00 kcal/kg C) (100. C- 20. C) ∆Q = 80. kcal = 80.kcal‧ J/cal = 396. kJ ∆Q = 80. kcal = 80.kcal‧ J/cal = 396. kJ Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Change of Phase and Latent Heat It requires an energy “investment” to change the phase from solid to liquid to gas. It requires an energy “investment” to change the phase from solid to liquid to gas. By breaking the bonds that hold atoms, they can have the same kinetic energy but different total energies. By breaking the bonds that hold atoms, they can have the same kinetic energy but different total energies. The energy to change the phase is “hidden” and therefore called “latent heat.” The energy to change the phase is “hidden” and therefore called “latent heat.” Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Latent heat ∆Q = mL For Water: Fusion (and melting) Fusion (and melting) L f = 333 kJ/kg = 79.4 kcal/kg Vaporization Vaporization L v = 2260 kJ/kg = 540 kcal/kg Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Work from a Heat Reservoir The work done by a system is equal to the loss of the internal energy. The work done by a system is equal to the loss of the internal energy. For an ideal gas For an ideal gas W = ∫ V1 V2 PdV Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

First Law of Thermodynamics ∆E = ∆Q -W Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Applications: Adiabatic (∆Q =0) ∆E = -W Isovolumetric (∆V =0) ∆E = ∆Q Isothermal (∆T =0) W =∫ V1 V2 PdV = ∫ V i V f ( nRT/V) dV W = n R T ln(V f /V i ) Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Mid Chapter Summary The internal energy is the total average energy of the atoms of an object.The internal energy is the total average energy of the atoms of an object. Heat is the change in internal energy. Heat is the change in internal energy. The change in temperature is proportional to the change in internal energy (heat flow) when there is no change of phase and the system does no work. The change in temperature is proportional to the change in internal energy (heat flow) when there is no change of phase and the system does no work. The first law of thermodynamics states The first law of thermodynamics states ∆E = ∆Q - W Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Conduction: P = kA |dT/dx | P = kA |dT/dx | Examples: Examples: – Thermos bottles – Blankets – Double pane windows – Newton’s law of cooling P = h A(T 2 – T 1 ) – Pans – R factor or R value P = A(T 2 – T 1 )/∑ i R i Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Convection: Heat transfer by material transfer Heat transfer by material transfer Forced convection (fluids) Forced convection (fluids) – External force produces material transfer Natural Convection Natural Convection – Buoyancy-driven flow – Newton’s law of cooling applied P = h A(T 2 – T 1 ) h depends on flow conditions Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Radiation: Stefan-Boltzmann Law Stefan-Boltzmann Law P = εσ AT 4 Wien’s LawWien’s Law P ∝T4P ∝T4P ∝T4P ∝T4 σ = x W/m 2 ‧K 4 σ = x W/m 2 ‧K 4 Emissivity 0< ε <1; ε ~ ½ Emissivity 0< ε <1; ε ~ ½ Reflectivity (albedo) R = (1- ε) Reflectivity (albedo) R = (1- ε) Energy balance Energy balance P in - εσ A(T ave ) 4 = 0 Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Global Warming?: P in = ( 1- ε λ ) P sun T ave = [( 1- ε λ ) P sun /( ε GH σA)] 1/4 Must understand every parameter to be accurate. Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Summary: Heat is transferred by Heat is transferred by o Conduction—energy diffusion o Convection—mass transport o Radiation—electromagnetic waves Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Guided Practice If the power per unit area (intensity) of sunlight on the earth is 1.0 kW/m 2 and the emissivity is 0.6, what is the expected avearge temperatue of the earth? Comment on the effect of a change in the emissivity or solar radiation. P in = ∫ 0 2π ∫ 0 π/2 I cos θ sin θ r 2 dθ dφ P in = I (2πr 2 ) (½ ) sin 2 θ | 0 π/2 = I (πr 2 ) = 1.0 kW/m 2 (3.14)(6.4x10 6 m) 2 = 1.3 x W P in = εσ A(T ave ) 4 T ave = [ P in / εσ A] 1/4 = [1.3 x /(0.6‧5.66 x10 -8 ‧ 5.1x10 14 )] 1/4 =294 K=21C Physics 1710 C hapter 20 Heat & 1 st Law of Thermo

Guided Practice If the power per unit area (intensity) of sunlight on the earth is 1.0 kW/m 2 and the emissivity is 0.6, what is the expected average temperature of the earth? Comment on the effect of a change in the emissivity or solar radiation. Physics 1710 C hapter 20 Heat & 1 st Law of Thermo