Lecture 3

Thermal Physics Lecture 3 – Heat, Specific Heat, First Law of Thermodynamics Textbook reference: 21.1, 21.4, 20.2, 19.5 “Feuer Frei” – Rammstein (Pyrotechnic effects from live shows) Last Pme in Physics… P V = nRT
moles P V = N kB T
molecules 2 1
⇒T =
( m0 v 2 )
3kB 2
Average translaPonal energy Degrees of Freedom Every kind of molecule has a certain number f of degrees of freedom, which are independent ways in which the molecule can store energy. What ways can molecules store energy? Monatomic (1 atom) eg. Helium f = 3 3
Energy = kB T
2
•  Can move in the x, y, z direcPon: can have KE in each of these direcPons (translaPonal) •  Classically: can rotate and have rotaPonal KE BUT Quantum effects mean that this is not detectable Diatomic (2 atoms) eg. O2 f = 7 7
Energy = kB T
2
•  Can move in the x, y, z direcPon: can have KE in each of these direcPons (translaPonal) •  Classically: can rotate about 3 axes Quantum: rotaPons only disPnguishable about 2 axes •  At room temperature: f=5/2 kBT •  Can vibrate: stores energy as PE and KE Note: We will come back to this later but below ~100K molecule does not rotate. Below ~ 1000K molecule does not vibrate Polyatomic (many atoms) eg. Methane CH4 •  Can move in the x, y, z direcPon: can have KE in each of these direcPons (translaPonal) •  Classically: can rotate about 3 axes •  Can vibrate in mulPple ways Note: We will come back to this later but below ~100K molecule does not rotate. Below ~ 1000K molecule does not vibrate Theorem of EquiparPPon of energy 1
Each degree of freedom contributes 2 k B T to the energy of a system, where possible degrees of freedom are those associated with translaPon, rotaPon, and vibraPon of molecules. 1
Total internal energy of a gas = f N kB T
2
3
Monatomic gas: Eint = N kB T
2
Internal Energy, E
int
, 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. v=0
Heat, Q Heat is defined as the transfer of energy across the boundary of a system due to a temperature difference between the system and its surroundings. Heat is transferred from the body at the higher temperature to the body at a lower temperature. Units = Joules, J Heat does not mean “hot” The heat that flows from hot to cold originates in the internal energy of the hot substance. It is not correct to say that a substance contains heat. QuesPon What is the difference between heat and internal energy? Heat is energy transferred from or into the system What is another way of transferring energy to a system? Work done on or by the system Joule’s experiment for determining the mechanical equivalent of heat. You can work out the gravitaPonal potenPal energy transferred to the water. This is how the calorie is determined! How much energy required to raise temperature of 1 gram of water by 1oC. 1 calorie = 4.186 J Fig. 20.1, p. 567 Heat Capacity •  The heat capacity, C, of a parPcular sample is defined as the amount of energy needed to raise the temperature of that sample by 1oC •  If energy Q produces a change of temperature of ΔT, then Q = C ΔT Specific Heat •  Specific Heat, c, is the heat capacity per unit mass; i.e. c=C/m •  If energy Q transfers to a sample of a substance of mass m and the temperature changes by ΔT, then the specific heat is Q
c≡
m ΔT
Specific Heat, c This relates the heat to the change in temperature of a substance: Q = mc∆T
‘c’ is called the “Specific Heat” of a substance. It is a measure of how insensiPve a substance is to the addiPon of energy. A beoer term would be “specific energy transfer” (recall definiPon of heat). Specific Heat, c In your textbook this is table 19.2 on page 556 Sign ConvenPons •  If the temperature increases: –  Q and ΔT are posiPve –  Energy transfers into the system •  If the temperature decreases: –  Q and ΔT are negaPve –  Energy transfers out of the system •  Can be tricky! Why does the Northern Hemisphere vary more over a year? (hint: think about specific heat of land vs. water) (hint2: Land can be grossly approximated as being composed of silicon in Table 19.2) Imagine you have 1 kg each of iron, glass, and water, all at 10°C. Rank the samples from lowest to highest temperature aqer 100J of energy is added to each sample. 1.  Iron 2.  Glass 3.  Water Imagine you have 1 kg each of iron, glass, and water, all at 10°C. Rank the samples from lowest to highest temperature aqer 100J of energy is added to each sample. 1.  Water 2.  Glass 3.  Iron Because water has the highest specific heat it has the smallest change in temperature, etc. D Demo Unit Hb7: thermal conducPvity •  Boiling water in a paper plate •  What do you expect to happen? Phase Changes •  A phase change is when a substance changes from one form to another –  Two common phase changes are •  Solid to liquid (melPng) •  Liquid to gas (boiling) •  During a phase change, there is no change in temperature of the substance •  We describe the amount of energy required to effect the change by the “Latent Heat” hop://www.atmo.arizona.edu/students/courselinks/fall07/nats101s31/lecture_notes/sep27.html Latent Heat, L •  Different substances react differently to the energy added or removed during a phase change due to their different molecular arrangements •  The amount of energy also depends on the mass of the sample •  If an amount of energy Q is required to change the phase of a sample of mass m, then L = Q /m Latent Heat, cont •  The quanPty L is called the latent heat of the material –  Latent means “hidden” –  The value of L depends on the substance as well as the actual phase change •  The energy required to change the phase is Q = ± mL
Latent Heat, final •  The latent heat of fusion is used when the phase change is from solid to liquid •  The latent heat of vaporisaBon is used when the phase change is from liquid to gas •  The posiPve sign is used when the energy is transferred into the system –  This will result in melPng or boiling •  The negaPve sign is used when energy is transferred out of the system –  This will result in freezing or condensaPon From Ice to Steam in 5 parts Part A: Warming Ice •  Start with one gram of ice at –30.0ºC •  During phase A, the temperature of the ice changes from –
30.0ºC to 0ºC •  Use Q = mi ci ΔT –  Find (exercise) that 62.7 J of energy are added Part B: MelPng Ice •  Once at 0ºC, the phase change (melPng) starts •  The temperature stays the same although energy is sPll being added •  Use Q = mi Lf –  Exercise: find the energy required is 333 J –  On the graph, the values move from 62.7 J to 396 J Part C: Warming Water •  Between 0ºC and 100ºC, the material is liquid and no phase changes take place •  Energy added increases the temperature •  Use Q = mwcw ΔT –  Exercise: find that 419 J are added –  The total energy added is now 815 J Part D Boiling Water •  At 100ºC, a phase change occurs (boiling) •  Temperature does not change •  Use Q = mw Lv –  Exercise: find this requires 2260 J –  The total is now 3070 J Note that the transiBon to steam dominates the total amount of energy required in all the 5 parts. Part E: HeaPng Steam •  Aqer all the water is converted to steam, the steam will heat up •  No phase change occurs •  The added energy goes to increasing the temperature •  Use Q = mscs ΔT –  Exercise: find that 40.2 J are needed –  The temperature rises to 120o C –  The total energy added is 3110 J From Ice to Steam in 5 parts 3110 J of energy added Calorimetry: Problem-­‐Solving Strategy •  Units of measurement must be consistent –  For example, if your value of c is in J/kg.oC, then your mass must be in kg, the temperatures in oC and energies in J •  Transfers of energy are given by Q =mc ΔT only when no phase change occurs •  If there is a phase change, use Q = mL •  Be sure to select the correct sign for all energy transfers: –  Remember to use Qcold = -­‐ Qhot –  The ΔT to use is always Tf -­‐ Ti (i.e. Final -­‐ IniBal Temp.) One other concept we need…. Energy (in a system) is always conserved. Any transfer of energy into or out of a system will result in a change in the internal energy of the system. There are two ways to transfer energy into or out of a system: heat and work. First Law of Thermodynamics ∆Eint = Q + W
Energy conservaPon: “you can’t win” QuesPon A thermodynamic system undergoes a process in which its internal energy decreases by 500 J. Over the same Pme interval, 220 J of work is done on the system. Find the energy transferred from it by heat.