James Joule and the mechanical equivalent of heat

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James Joule and the mechanical equivalent of heat

• Joule knew a mass above the ground had potential energy. He dropped an object on a cord, turning a paddle in water monitored by a very accurate thermometer.

• His conclusion was to connect energy conservation (potential and kinetic) to heat as a third form observed.


Specific heat

• A specific heat value reveals how much temperature will change when a given amount of a substance absorbs a given amount of heat.

• Water is a “benchmark” as one ml of water will absorb 1 cal of heat to raise its temperature by 1oC.


Specific heat values


You put 1 kg of the following materials on a bunsen burner. Which one’s temperature rises the least?

A. Aluminum, c = 910 J/kg K

B. Berillium, c = 1970 J/kg K

C. Copper, c = 390 J/kg K

D. Water, c = 4190 J/kg K

Q17.3.5


A. Aluminum, c = 910 J/kg K

B. Berillium, c = 1970 J/kg K

C. Copper, c = 390 J/kg K

D. Water, c = 4190 J/kg K

A17.3.5

You put 1 kg of the following materials on a bunsen burner. Which one’s temperature rises the least?


• A 500W heater dumps all its energy into heating 1kg of water in a teapot. How long does it take to heat the water to boiling if the water started out at room temperature?

• How many moles of water is this?

• cwater = 4190 J/kg K

• Mwater = 0.018 kg/mol

Water in a teapot


Phase changes and temperature behavior• A solid will absorb heat according to its heat

capacity, becoming a hotter solid.

• At the melting point, a solid will absorb its heat of fusion and become a liquid. An equilibrium mixture of a substance in both its liquid and solid phases will have a constant temperature.

• A cold liquid will absorb heat according to its heat capacity to become a hotter liquid.

• At the boiling point, a liquid will absorb its heat of vaporization and become a gas. An equilibrium mixture of liquid and gas will have a constant temperature.

• A cold gas can absorb heat according to its heat capacity and become a hotter gas.


You wish to increase the temperature of a 1.00-kg block of a certain solid substance from 20°C to 25°C. (The block remains solid as its temperature increases.) To calculate the amount of heat required to do this, you need to know

A. the specific heat of the substance.

B. the molar heat capacity of the substance.

C. the heat of fusion of the substance.

D. the thermal conductivity of the substance.

E. more than one of the above

Q17.4


A. the specific heat of the substance.

B. the molar heat capacity of the substance.

C. the heat of fusion of the substance.

D. the thermal conductivity of the substance.

E. more than one of the above

A17.4

You wish to increase the temperature of a 1.00-kg block of a certain solid substance from 20°C to 25°C. (The block remains solid as its temperature increases.) To calculate the amount of heat required to do this, you need to know


Hot pot

• A heavy copper pot of mass 2 kg is at temperature of 150C. You pour 0.1 kg of water at 25C into the pot then quickly close the lid so no steam can escape. Find the final temperature of the pot and its contents and determine the phase (liquid or gas) of the water. Assume no heat is lost to the surroundings.

• cwater = 4190 J/kg K, ccopper = 390 J/kg K

• Lwater = 2256 x 103 J/kg


Why, and how well, do materials transfer heat?

• Conduction: heat transfer within a body or between two bodies in contact.

• Convection: heat transfer through movement of mass from one place to another

• Radiation: heat transfer by electromagnetic radiation


Conduction of heat I

• You bring a cooler to the beach to keep some tasty beverages cold. The cooler has a total wall area of 0.8 m2 and a wall thickness of 2.0 cm. It is filled with ice, water and your tasty beverage at 0C. What is the rate of heat flow into the cooler if the outside wall is at 30C?

• How much ice melts in 8 hours?


Convection of heat

• Heating by moving large amounts of hot fluid, usually water or air.

• Figure 17.28 at right illustrates heat moving by convection.


Symbols, signs, and definitions for heat and workHot coffee is poured into a room-temperature mug and over

time, they reach thermal equilibrium.

• What is the sign of Q for the coffee?

• Sign of Q for mug?

• What is Q and the sign of work for a coffee mug, if it slides along a table with friction (might help to consider what happens to thermal energy of cup)?


Does the path of the PV change matter?• The start, the finish, and the shape of the curve are all

significant.


Compressed airA compressed air cartridge at a starting pressure of p1 = 50 atm and

starting volume V1 = 5 cm3 is put into an empty, sealed balloon. It pops and causes the balloon to expand to 10 times the volume of the cartridge, V2.

• Assuming the air undergoes an isothermal expansion and behaves like an ideal gas, draw the pV diagram of this process.

• What is the final pressure of the balloon?

• Two other ways different than the first method 1) of inflating the balloon to the same final volume are 2) a constant pressure p1 = 50 atm inflates the balloon from V1 to V2 or 3) a constant pressure p2 (calculated above) inflates the balloon from V1 to V2. Draw pV diagrams and rank the work done by the expanding air for the three cases of isothermal expansion.


Signs of heat and work on a systemIs the work W, the heat Q, and the change in thermal energy Eth, positive (+), negative

(-) or zero (0) for the following situations?

Does the temperature increase (+), decrease (-), or stay the same (0)

W Q Eth T

1. You hit a nail with a hammer

2. You hold a nail over a Bunsen burner

3. You compress the air in a bicycle pump by pushing down on the handle very rapidly

4. You turn on a flame under a cylinder of gas, and the gas undergoes an isothermal expansion

5. A flame turns liquid water into steam

6. High pressure steam spins a turbine

7. Steam contacts a cold surface and condenses


Expanding Helium

Helium gas starts at a volume Vi = 1L and Pi = 1 atm. It expands linearly to Vf = 3L and Pf = 3 atm.

1. Draw the pV diagram for this process

2. What is the work done by the gas when it expands?

3. What is its increase in internal energy?

4. How much heat is gained or lost by the gas?


Condensing steam

1671 cm3 of steam condenses to form 1 gram of water (1 cm3) when held at a constant pressure of 1 atm (1.013 x 105 Pa). The heat of vaporization at this pressure is Lv = 2.256 x 106 J/kg.

1. Draw the pV diagram for this process

2. What is the work done by the water when it condenses?

3. What is its increase in internal energy?


Cyclic processes and isolated systems• Consider Problem-Solving Strategy 19.1.

• Follow Example 19.2.


Study of thermodynamic processes

• The cyclic process shown proceeds counterclockwise from a in the pV diagram to b and back and the total work is W = -500J.

• Why is the work negative?

• Find the change in internal energy and the heat added during this process


Note the definitions on page 657• Adiabatic

• Isochoric

• Isobaric

• Isothermal


The processes on a PV diagram• Notice the subtle differences for each curve in Figure 19.16.


Adiabatic changes• In an adiabatic process, no heat is transferred from system and

surroundings.


Cyclic processA cyclic thermodynamic process

occurs as shown, where path c-b is isothermal. Draw isotherms to determine temperatures of states a, b, c. Predict the Q, W and Eth for each process:

What changes if c-b is adiabatic?

Q W Ua-c

c-b

b-a

Whole cycle


Adiabatic and isothermal processesAn ideal gas at Pi = 1 atm and Vi = 1m3 doubles

its volume A isothermally and B adiabatically

• Draw a PV diagram for both processes• What is the final pressure for process

A and B?• Compute W, Eth and Q for each

process.


Measuring heat capacities• Heat capacities may be

measured at constant volume in a fairly complex process using a bomb calorimeter.

• Heat capacities may be measured at constant pressure using equipment as simple as a coffee cup.


Relating heat capacities at constant volume and pressure


Heat capacities tabulated for selected gasses

James Joule and the mechanical equivalent of heat

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