1. Ch 12 - Heat
This false-color thermal image (an infrared photo) shows where energy is escaping from a house by heat transfer, because it is colder outside than inside. In this chapter we investigate the connection between heat and energy.
Chapter Goal: To expand our understanding of energy to include the energy transfer mechanism of heat.

2. 12.2 The Kelvin Temperature Scale
A constant-volume gas
thermometer.

3. 12.2 The Kelvin Temperature Scale
absolute zero point = oC

4. Our model of energy: Emech = K + U
In this chapter, we will look at another kind of energy, and another kind of energy transfer function.

5. Internal Energy, Uint
Let’s look at another type of energy of a system, its internal energy, Uint. This consists of :
microscopic motion of atoms and molecules
potential energy of molecular bonds
Uint can be transferred in or out of a system, via a non-mechanical energy transfer function called HEAT (Q).

6. Heat (Q) is an energy transfer mechanism that operates when the system is put in contact with a hotter or colder environment

7. Heat, Temperature, and Thermal Energy
Internal Energy Uint is an energy of the system due to the   motion of its atoms and molecules. Any system has an   internal energy even if it is isolated and not interacting with its environment. The units of Uint are Joules.
Heat Q is energy transferred between the system and the   environment as they interact due to a temperature difference between them. A temperature difference is required in order for heat to be transferred between the system and the environment. The units of Q are Joules.
Temperature T is a state variable that quantifies the   “hotness” or “coldness” of a system. The units of T  are degrees Celsius or Kelvin. Temperature is not the same as heat

8. Heat and Equilibrium Temperature
Heat (Q) is an energy transfer mechanism analogous to work.
Energy is transferred by work when force is applied (macroscopic).
Energy is transferred by heat (Q) when collisions occur between faster moving molecules and slower moving molecules (microscopic).
Energy transfer via heat will stop when all interacting objects are at the same temperature.

9. The sign of heat, Q

10. Heat added to the system
If energy is added to the system due to heat only, and the system is not moving, the increase in energy will manifest itself in one of two ways:
change in temperature
change in phase

11. Temperature Change and Specific Heat Capacity
The temperature change of a substance due to heat is:
∆T = Q/(mc)
where Q is heat (in joules), m is mass (in kg) and c is called the specific heat capacity of that substance. The symbol for specific heat capacity is c.
The specific heat capacity is the amount of energy that raises the temperature of 1 kg of a substance by 1 K (or 1 °C) and has units of Joules/kg K or Joules/kg °C. The above equation is often written:
Q = mc ∆T

12. Specific heat capacity problem
The specific heat capacity of gold (cgold) = 129 J/kg K. How much heat is required to raise the temperature of 500 g of gold from 100 to 500 C?

13. Specific heat capacity problem
The specific heat capacity of gold (cgold) = 129 J/kg K. How much heat is required to raise the temperature of 500 g of gold from 100 to 500 C?
Answer: Q = 2580 Joules
It was not necessary to convert to Kelvin since the calculation requires ΔT.

14. Objects A and B are brought into close thermal contact with each other, but they are well isolated from their surroundings. Initially TA = 0°C and TB = 100°C. The specific heat of A is more than the specific heat of B. The two objects will soon reach a common final temperature Tf. The final temperature is:
Tf > 50°C.
Tf < 50°C.
Tf = 50°C.
Answer: B 14

15. Tf > 50°C. Tf < 50°C. Tf = 50°C.
The energy transferred from A is equal to that of the energy transferred to B. Since Q = cm ΔT, and cA < cB , the magnitude of ΔTB > ΔTA .
Therefore the final temperature of both blocks is less than 50˚.
Tf > 50°C.
Tf < 50°C.
Tf = 50°C.
Answer: B 15

16. EOC #51
A 0.25-kg coffee mug is made from a material that has a specific heat capacity of 950 J/(kg · C°) and contains 0.30 kg of water. The cup and water are at 25° C. To make a cup of coffee, a small electric heater is immersed in the water and brings it to a boil in two minutes. Assume that the cup and water always have the same temperature and determine the minimum power rating of this heater.
Qh = mw cw ∆Tw + mc cc ∆Tc

17. EOC #51
A 0.25-kg coffee mug is made from a material that has a specific heat capacity of 950 J/(kg · C°) and contains 0.30 kg of water. The cup and water are at 25° C. To make a cup of coffee, a small electric heater is immersed in the water and brings it to a boil in two minutes. Assume that the cup and water always have the same temperature and determine the minimum power rating of this heater.
Qh = mw cw ∆Tw + mc cc ∆Tc
P = 930 W

18. Calorimetry – Conservation of Energy
Two (or more) systems, at different temperatures are placed in contact, but isolated from the environment.
These systems will eventually reach a common equilibrium temperature without energy loss.

19. Problem-solving strategy for Calorimetry Problems
Identify the interacting systems and verify that they are isolated from the environment (Code language: insulated container).
List known information and identify what you need to find. Convert quantities to SI units, and volumes to mass.
Calorimetry problems are a statement of conservation of energy:
Qnet = Q1 + Q2 + Q3 + … = 0
Q = m c (Tf – T0) for each system. Do not automatically put the higher temperature first! Assess your answer. Tf that is higher or lower than all initial conditions is an indication of an error, usually with signs.

20. Calorimetry example with 3 materials
A precious stone dealer wishes to find the specific heat capacity of a kg gemstone. The specimen is heated to 95.0° C and placed in a 0.15 kg copper vessel containing kg water at equilibrium (with the copper) at 25.0°C. There is negligible loss to the environment. When equilibrium is established (with the gemstone), the temperature is 28.5°C. What is the specific heat capacity of the gemstone?

21. Calorimetry example with 3 materials
A precious stone dealer wishes to find the specific heat capacity of a kg gemstone. The specimen is heated to 95.0° C and placed in a 0.15 kg copper vessel containing kg water at equilibrium (with the copper) at 25.0°C. There is negligible loss to the environment. When equilibrium is established (with the gemstone, the temperature is 28.5°C. What is the specific heat capacity of the gemstone?
Answer: 689 J/kg K

22. Phase Change and Latent Heat

23. Phase change and latent heat
A phase change is characterized by a change in thermal energy without a change in temperature.
The temperature vs. heat graph shows that during the phase changes, the temperature does not change, although heat energy continues to be added.

24. Phase Change and Latent Heat
The amount of heat energy that causes 1 kg of substance to undergo a phase change is called the latent heat of that substance.
The symbol for latent heat of transformation is L.
The units of latent heat are Joules/kg.

25. Phase Change and Latent Heat
It takes more energy to change a liquid into a vapor, than to change a solid into a liquid.
To do the former, we use the latent heat of vaporization, Lv.
To do the latter, we use the latent heat of fusion, Lf.

26. Phase Change and Latent Heat
The heat required for the entire system of mass m to undergo a phase change is:
Q = ±mLf melt/freeze
Q = ±mLv evaporate/condense
the ± sign indicates that heat must be added to the system during melting and evaporation and removed from the system during freezing and condensation.

27. Latent Heats of fusion and vaporization: It takes a lot of energy to change phase

28. EOC #67
Ice at -10.0°C and steam at 130°C are brought together at atmospheric pressure in a perfectly insulated container. After thermal equilibrium is reached, the liquid phase at 50.0°C is present. Ignoring the container and the equilibrium vapor pressure of the liquid at 50.0°C, find the ratio of the mass of steam to the mass of ice. The specific heat capacity of steam is 2020 J/(kg · C°), the specific heat capacity of ice is 2.00 x103 J/(kg·C°), and the specific heat capacity of water is 4186 J/(kg·C°).

29. EOC #67
Ice at -10.0°C and steam at 130°C are brought together at atmospheric pressure in a perfectly insulated container. After thermal equilibrium is reached, the liquid phase at 50.0°C is present. Ignoring the container and the equilibrium vapor pressure of the liquid at 50.0°C, find the ratio of the mass of steam to the mass of ice. The specific heat capacity of steam is 2020 J/(kg · C°), the specific heat capacity of ice is 2.00 x103 J/(kg·C°), and the specific heat capacity of water is 4186 J/(kg·C°). Ans: .223

30. Prelab Question #2
You have 100 g of water in an aluminum calorimeter cup that has a mass of 25 g. Both water and aluminum have come to thermal equilibrium at 21° C. What will be the final temperature of the mixture if 10 g of 0 ° ice is added?