Physics 111. Lecture 35 (Walker: ) Latent Heat Internal Energy First Law of Thermodynamics. Latent Heats. Latent Heat

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1 Physics 111 Lecture 35 (Walker: ) Latent Heat Internal Energy First Law of Thermodynamics Latent Heats The heat required to convert from one phase to another is called the latent heat. The latent heat, L, is the heat that must be added to or removed from one kilogram of a substance to convert it from one phase to another. During the conversion process, the temperature of the system remains constant. Dec. 9, 2009 Lecture 35 1/28 Lecture 35 2/28 Latent Heat Heat of fusion, L F : heat (in J) required to change 1.0 kg of material from solid to liquid Heat of vaporization, L V : heat (in J) required to change 1.0 kg of material from liquid to vapor For melting a mass m of material that is already at the melting temperature, the heat required is Q = ml F For vaporizing a mass m of material that is already at the boiling point, the heat required is Q = ml V Lecture 35 4/28

2 Example How much heat must be removed from 2 kg of water at 0 C in order to freeze it? Phase Change & Energy Conservation Solving problems involving phase change is like solving problems involving heat transfer, except that the latent heat must be included. Q = ml F = (2 kg)(334 kj/kg) = 668 kj During the time the water is freezing, the temperature will stay at 0 C. Lecture 35 5/28 Lecture 35 6/28 Problem Solving: Calorimetry with Phase Change Example: 0.1 kg of ice at -10 C added to 1 kg of water at 30 C. Final temperature T f of system? 1. Is the system thermally isolated (no heat in or out of system)? If so, 2. Apply conservation of energy to system: Q lost- Water = Q gained-ice 3. If no phase changes occur for one part, heat transferred will depend on mass, specific heat, and temperature change of that part. (T in C ok) Q lost-water = m W c W (T Wi -T f ) 4. If there are, or may be, phase changes, latent heat must be considered. Determine or estimate what phase each part of final system will be in. We assume all ice melts; no initial water freezes. Q gained-ice = m I c I ( C)+ m I L F + m I c W T f 5. Temperature change and latent heat terms for one part of system should all be on one side of equation; all temperature changes are positive. 6. There is only one final temperature T f (same for all parts) when system reaches equilibrium. 7. Solve. If answer doesn t make sense (final system all water at -5 C), initial phase assumptions were wrong. Recalculate.

3 Example 0.1 kg of ice at -10 C added to 1 kg of water at 30 C. Final temperature T f of system? (Assume water does not freeze and all ice melts.) Q lost-water = Q gained-ice m W c W (T Wi - T f ) = m I c I (10 C)+ m I L F + m I c W T f (1kg)(4.186 kj/kg-k)(30 C-T f ) = =(0.1kg)[(2.09kJ/kg-K)(10 C)+334 kj/kg +(4.186kJ/kg-K)T f ] T F = 19.7 C (Original phase assumptions valid) Lecture 35 9/28 Internal Energy U The internal energy U of an object is the sum total of all the random kinetic and potential energies of all the atoms/molecules in the object. The amount of internal energy depends on (a) the temperature, has more internal energy than (b) the number of molecules, (c) the type of molecules, and (d) the internal potential energy associated with interactions. Lecture 35 10/28 Internal Energy U The sum total of all the energy of all the molecules in a substance is its internal (or thermal) energy U. Temperature: measures molecules average random kinetic energy Internal energy U: total energy of all molecules (excluding external kinetic & potential energy) Heat Q: transfer of energy due to difference in temperature Internal Energy An ideal gas has no internal potential energy since there are no interactions between molecules. The internal energy U is all kinetic, and for a monatomic gas, is : But since we know the average kinetic energy in terms of the temperature, we can write: where n is the number of moles of gas.

4 Internal Energy - Molecular Gas If gas is molecular rather than atomic, rotational and vibrational kinetic energy need to be taken into account. (a) Internal Rotational KE 1 N Iω 2 2 Internal Potential Energy Molecules in liquids and solids DO interact, so in those phases, there is internal potential energy. Water in the water vapor state at 100 C will have more internal potential energy than liquid water at the same temperature. The internal potential energy difference per kg is the Latent Heat of Vaporization (as we saw earlier). Likewise, water in the liquid state at 0 C will have more internal potential energy than ice at the same temperature. The internal energy difference per kg is the Latent Heat of Fusion. (b) Internal Vibrational KE and PE Lecture 35 14/28 Chapter 18 The Laws of Thermodynamics First Law of Thermodynamics The first law of thermodynamics is a statement of the conservation of energy that includes energy transferred as heat (Q). If a system s volume is constant, and heat is added, its internal energy increases. Lecture 35 15/28 Lecture 35 16/28

5 First Law of Thermodynamics If a system does work on the external world, and no heat is added, its internal energy decreases. First Law of Thermodynamics Combining these gives the first law of thermodynamics. The change in a system s internal energy is related to the heat in, Q, and the work done, W, as follows: It is vital to keep track of the signs of Q and W. Lecture 35 17/28 Lecture 35 18/28 The First Law of Thermodynamics The change in internal energy of a closed system will be equal to the energy added to the system minus the work done by the system on its surroundings. This is the law of conservation of energy, written in a form useful to systems involving heat transfer. Example While 100J of heat is added to a cylinder containing gas, the gas does 80J of work by pushing up a piston. (a) Does the internal energy of the gas increase or decrease? How much? (b) Will the temperature of the gas increase? Lecture 35 19/28 Lecture 35 20/28

6 Human Metabolism and the First Law If we apply the first law of thermodynamics to the human body: Human Metabolism and the First Law The metabolic rate is the rate at which internal energy is transformed in the body. we know that the body can do work. If the internal energy is not to drop, there must be energy coming in. It isn t in the form of heat; the body loses heat rather than absorbing it. Rather, it is the chemical potential energy stored in foods. Lecture 35 21/28 Lecture 35 22/28 End of Lecture 35 For Friday, Dec. 11, read Walker 18.8, Homework Assignment 17b is due at 11:00 PM on Saturday, Dec. 12. Lecture 35 23/28