Ch. 11  Heat

 

11.1 Heat and Internal Energy

 

Internal Energy U  the energy associated with the microscopic kinetic (translational, vibrational, and rotational) and potential (intermolecular forces) energies of the system.

 

Heat is a mechanism by which energy is transferred between a system and its environment because of a temperature difference between them. We will thus not talk about how hot something is, but how much energy Q is transferred to a system due to a temperature difference.

 

Heat is thermal energy, the ability to change the T of a system in contact.

 

Historical Unit: calorie

 

            1 calorie is the energy necessary to raise the temperature of 1 g of water from 14.5°C to 15.5°C.

 

Note: the familiar “Calorie” used in determining the chemical energy of food is actually 1 kcal (1000 cal).

 

Mechanical Equivalent of Heat
 1 cal ≡ 4.186 J    or        1 Cal ≡ 4186 J

 

Example: Problem 7

 

A 75.0 kg weight-watcher wishes to climb a mountain to work off the equivalent of a large piece of chocolate cake rated at 500 (food) Calories. How high must the person climb? (1 food Calorie = 103 calories).

 

11.2 Specific Heat

 

Some substances require more/less than 4.186 J to raise 1 g by 1°C (or 4186 J for 1 kg by 1°C). We use specific heat to describe and quantify this fact.

 

where . NOTE ORDER!

 

By definition, the specific heat for water is c = 4186 J kg-1 °C-1.

 

So the energy required to raise the temperature of a system of mass m by ΔT is:

 

 

 

 

Sign Convention:

 

When T in a system increases, energy flowing into the system - Q and ΔT are positive

When T in a system decreases, energy flowing out of the system - Q and ΔT are negative

 

Application: Sea breezes

 

Specific heat of sand is lower than that of water. Daytime heating causes breeze from sea to land as hot air rises over the sand.

 

Exercise: Problem #2

 

A 50 g sample of copper is at 25°C. If 1,200 J of energy is added to the copper by heat, what is its final temperature?

 

Quick Quiz 11.1

Imagine you have 1 kg each of iron, glass, and water, and that all of the samples are at 10°C.  (a) Rank the samples from lowest to highest temperature after 100 J is added to each by heat. (b) Rank them from least to greatest amount of energy transferred by heat if enough energy is transferred so that each increase in temperature by 20°C. 
11.3 Calorimetry

Suppose we put a warm object into cooler water:

 

 

For any isolated system exchanging heat amongst its components:

 

Here,

 

 

Sign Convention:

 

The energy transfer  is negative because energy is leaving the hot substance. The minus sign in  insures that  is positive, since it is the cold object that is gaining energy. Note that . This is may be easier to remember.

 

Example: Problem 15

 

An aluminum cup contains 225 g of water and a 40-g copper stirrer, all at 27°C. A 400 g sample of silver at an initial temperature of 87°C is placed in the water. The stirrer is used to stir the mixture gently until it reaches its final equilibrium temperature of 32°C. Calculate the mass of the aluminum cup.

 

Example: Problem 18

 

A combination of 0.250 kg of water at 20.0°C, 0.400 kg of aluminum at 26.0°C , and 0.100 kg of copper that is at 100°C is mixed in an insulated container and allowed to come to thermal equilibrium. Neglect any energy transfer to or from the container and determine the final temperature of the mixture.
10.4 Latent Heat & Phase Change

 

Phase Changes:           vaporliquid              boiling/condensing

liquidsolid               melting/freezing

vaporsolid                sublimation

solid1solid2

 

Energy associates with phase change , where L is the latent heat of the substance for that particular phase change.

 

Sign Convention:

 

 

Heat of fusion  melting/freezing

Heat of vaporization  boiling/condensing

Heat of sublimation

 

 

Remember, in solving problems:

 

  1. consistent units
  2.  only if no phase change

ssigns, and that  has bee absorbed into the  sign in fron (and ssigns, and that  has bee absorbed into the  sign in fron (and  (solidliquid);

 (liquidvapor)

  1. remember ± signs, and that  

 

 

 

Example: Taking ice at T=-30.0°C to vapor at T=120.0°C (at constant pressure)

 

 

Part A. Warming ice, T changes  

 

Part B. Melting ice, T constant  

 

Part C. Warming water, T changes  

 

Part D. Vaporizing water, T constant  

 

Part E. Warming vapor. T changes  

 

Exercise: Problem 23

 

What mass of steam that is initially at 120°C is needed to warm 350 g of water and its 300-g aluminum container from 20°C to 50°C?

 

 

11.5 Thermal Conduction

 

Conduction  net transfer of energy due to vibrational motions of atoms, molecules, and (in the case of electrical conductors) mobile electrons without a net flow of the material.

 

 

 

 

Can you think of another example where the flow goes inversely with the “resistance”?

Example: Problem #39

 

A copper rod and an aluminum rod of equal diameter are joined end to end in good thermal contact. The temperature of the free end of the copper rod is held constant at 100°C, and that of the far end of the aluminum rod is held at 0°C. If the copper rod is 0.15m long, what must be the length of the aluminum rod so that the temperature at the junction is 50°C?

 

 

 

 

 

11.6 Convection

 

Convection  heat transfer by macroscopic movement of matter.

 

Natural Convection  lower density creates buoyancy - heated roadways, campfires, etc.

 

Forced Convection  using fans, pumps, etc.  some heating systems

 

 

Mathematically, convection is very difficult to deal with  far beyond the scope of this course! (Notice that the textbook has NO problems for this section!)

11.7 Radiation

 

All objects with T > 0 K radiate electromagnetic radiation at a rate of:

 

An object in radiative “contact” with surroundings at temperature T0 will absorb an amount of energy

 

So the net gain/loss of energy by radiation is

 

(Actually it’s a little more complicated than this, because here we have assumed that “e” is the same for the absorption and emission  i.e. that the absorption and emission occur over the same wavelength ranges.)

 

 

Thermogram of a human.

File written by Adobe Photoshop® 5.0

Example: Problem 11.44

Calculate the temperature at which a tungsten filament that has an emissivity of 0.25 and a surface area of 2.5x10-5 m2 will radiate energy at a rate of 25 W in a room where the temperature is 22°C.

 

11.8 Resisting Energy Transfer

 

 

 

 

Thermos bottles (more appropriately called Dewar flasks) help thermally isolate their contents thermally from the rest of the world.

 

 

The Hubble Space Telescope reduces T fluctuations from entering & exiting the Earth’s shadow using a blanket of highly reflective insulation.

 

11.9 Global Warming & Greenhouse Gases

 

The low “e” in the infrared due to various gases raises the T of the earth above what it would be in the absence of an atmosphere. This “greenhouse effect” is a misnomer, as real greenhouses get most of their T increase from inhibiting convective energy transport.

 

 

 

CO2, one of the major greenhouse gases, is on the rise. A doubling of CO2 could lead to a global increase in T of 2°C (according to one estimate), which could have a significant impact on the climate of the Earth.

 

In addition to CO2, CH4, N2O, and SO2 contribute.

 

2/3 of the greenhouse effect is due to H2O!! This was not included in climate models until about 10 years ago.

 

 

 

There is some evidence that the Earth is warming slightly in the past century (although not all parts of the atmosphere seem to be doing the same thing, so it is complex). Changes in solar irradiation may also be contributing to this trend.