9 Heat & Thermal Energy

HEAT AND THERMODYNAMICS

By : Arra C. Quitaneg

HEAT AND THERMODYNAMICS

OBJECTIVES:

- Define heat, temperature, specific heat capacity.

- Solve problems on thermal expansion heat transfer, quantity of heat and temperature conversion.

- Describe different heat transfer mechanisms.

What is temperature?

TEMPERATURE

• http://ippex.pppl.gov/interactive/fusion/controlatomtemp.html

- A quantity that tells how warm or cold an object is with respect to a standard

- related to the random motion of the molecules in a substance.

- it is proportional to the average kinetic energy of molecular translational motion.

Kelvin Scale

named after British physicist Lord Kelvin

Zero is assigned to the lowest possible temperature absolute zero

- 2730C

Celsius Scale

Named after a Swedish astronomer Anders Celsius

Zero is assigned to the temperature at which water freezes, and 100 is the temperature at which water boils.

Farenheit Scale

Named after a German physicist G.D Farenheit

32 is assigned to the temperature at which water freezes

212 is assigned to the temperature at which water boils.

TEMPERATURE SCALE CONVERSION

• °C = K - 273.15°

• K = °C + 273.15

°C = (°F - 32°)/1.8

°F= 1.8•°C + 32°

• Internal energy = the grand total of all energies inside a substance.

THERMAL EQUILIBRIUM

Objects that are in thermal equilibrium are at the same temperature.

A B

THERMAL EXPANSION

Why are there thermal

expansion joints in

roads?

-When the temperature of a substance is increased, molecules or atoms move faster and tend to move farther apart, resulting to an expansion of the substance.

-Expansion of liquids is greater than the expansion of solids.

How does a thermometer

work?

Is the expansion of

the liquid same as that of the glass?

THERMOMETER

Linear Expansion

• ∆L = change in length

• = coefficient of linear expansion

• L0 = initial length of the material

• ∆T = is the change in temperature

Volume expansion

• ∆V = change in volume

• = coefficient of volume expansion

• V0 = initial volume of the material

• ∆T = is the change in temperature

Problem-solving

• You place a small piece of melting ice in your mouth. Eventually, the water all converts from ice at T1= 320F to body temperature T2= 98.60F. Express the temperatures in 0C and in K and find T in both cases.

Solution:0F to 0C

°C = (°F - 32°)/1.8

°C = (32°F - 32°)/1.8

= 0°C

°C = (98.6°F - 32°)/1.8

= 37°C

K = °C + 273.15

K = 0°C + 273.15 = 273.15K

K = 37 °C + 273.15 = 310.15K

Solution:

T = T2-T1

T = 370C - 00C

= 370C

T = 310.15 K – 273.15K

= 37 K

Problem-solving

• A surveyor uses a steel measuring tape that is exactly 50 m long at a temperature of 200C. What is its length on a hot summer day when temperature is 350C. steel = 1.2x10-5 K-1

• SOLUTION

• Lf – L0= L0T

• Lf = L0T + L0

• Lf = L0 ( T + 1)

• Lf = 50m (1.2x10-5 K-1 15K + 1)

• Lf = 50.009 m

• A gas flask with volume 200cm3 is filled to the brim with mercury at 200C. How much mercury overflows when the temperature of the system is raised to 1000C? glass = 0.4 x10-5 K-1 mercury = 18 x 10-5 K-1

.

Solution:

glass = 3Vglass = 3(0.4 x10-5 K-1 ) 200 cm3 80K

Vglass = 0.192 cm3

Vmercury = (18 x10-5 K-1 ) 200 cm3 80K

Vmercury = 2.88 cm3

Solution:

Volume of mercury which overflows

Vmercury - Vglass

=2.88 cm3 - 0.192 cm cm3

= 2.69 cm3

• Solution

• = L/L0 T

• = (40.148cm – 40.125cm) /

(40.125cm)(450C - 200C)

• = 2.29 x 10-5 K

• A metal rod is40.125 cm long at 200C and 40.148 cm long at 450C. Calculate the average coefficient of linear expansion of the rod.

• A machinist bores a hole of diameter 1.350 cm on a steel plate at a temperature of 250C. What is the cross section area of the hole at a) 25 0C. B) when temperature of the plate is increased to 175 0C.

• An iron ring is to fit snugly on a cylindrical iron rod. At 200C, the diameter of the rod is 6.445 cm and inside diameter of the ring is 6.420 cm. To slip over the rod, the ring must be slightly larger than the rod by 0.008 cm. To what temperature must the ring be brought if its hole is to be large enough so it will slip over the rod.

Seatwork1. A gas flask with volume 1000cm3 at 0 0C is

completely filled with mercury at this temperature. How much mercury overflows if the flask is warmed at 550C? glass = 0.4 x10-5

K-1 mercury = 18 x 10-5 K-1

2. The steel bed of suspension bridge is 200 m long at 200C. If the extremes of temperature to which it might be exposed are – 30 0C to + 400C, how much will it contract and expand?

3. What is the change in length of a column of mercury 3.0 cm long if its temperature increases from 370 to 400 C? mercury = 60 x10-6

/ C0

4. A concrete highway is built of slabs 14 m long (200C). How wide should the expansion cracks be (at 200C) between slabs to prevent buckling if the range of temperature is -300C to 50 0C.

concrete = 12 x10-6 K-1

THERMAL EXPANSION OF WATER

THERMAL EXPANSION OF WATER

Water is densest at 40C.

As the water is cooled below 4 deg C however, it expands!

If water were like most other materials, the very

cold water would sink and lakes would freeze from the

bottom up.

Why is it that some foods remain hotter

much longer than others?

• The quantity of heat required to change the temperature of a unit mass of the substance by 1 deg Celsius.

• Thermal inertia- resistance of a substance to change its temperature

Quantity of Heat

• Q = amount of heat (1kcal = 4186J)

• m= mass

• c=specific heat capacity

• T = change in temperature

• If Q and T 0, heat enters the body and its temperature increases

• If Q and T 0, heat leaves the body and its temperature decreases

Other cause of Temperature Change

• Work can also be converted into heat.

• ½ PE = Q

• PE = potential energy

• Q = heat

• A certain amount of heat Q will warm 1 g of material A by 3 C0 and 1 g of material B by 4 C0

. Which material has the greater specific heat capacity?

Problem- solving:

1. How much heat is required to raise the

temperature of an empty 20 kg vat made of

iron from 100C to 900C?What if the vat is

filled with 20 kg of water? Ciron = 450 J/kgC0

C water = 41860C

2. What is the specific heat of a metal substance

if 135kJ of heat is needed to raise 5.1 kg of

the metal from 200C to 300C?

Problem- solving:1. How much heat is needed to increase the

temperature of 200 g of water by 50C? How much heat is needed to increase the temperature of 200 g lead by 50C? Clead = 0.03 kcal/kgC0 C

water = 1.00 kcal/kgC0

2. If a lead ball is dropped , its temperature increases when it strikes the ground. The original gravitational potential energy of the ball is converted to kinetic energy during the fall and then to thermal energy. Calculate the temperature increase of a lead ball dropped from a height of 20m. Clead = 0.03 kcal/kgC0

Seatwork

1. How many calories of heat would be required

to raise the temperature of a 45 kg person by

20C? Chuman body = 0.83 kcal/kgC0

2. When a scalpel is sterilized, its temperature

may rise to 150 0C. Calculate the amount of

heat in calories that must be removed from a

30 g steel scalpel to reduce its temperature

from 1500C to 200C? Csteel= 0.11 kcal/kgC0

Problem- solving:

2. If a lead ball is dropped , its temperature

increases when it strikes the ground. The

original gravitational potential energy of the

ball is converted to kinetic energy during the

fall and then to thermal energy. Calculate the

temperature increase of a lead ball dropped

from a height of 20m. Clead = 0.03 kcal/kgC0

Calorimetry and Phase Change

• Calorimetry – measuring heat

• Phase – state of matter

Q= quantity of heat

m=mass

L = latent heat of fusion or

vaporization

Phase change

Evaporation

How is fire-walking possible?

Why do dogs pant?

Evaporation• Evaporation is a change of phase from liquid to

gas.

• Cooling process

• Endothermic – heat is absorbed

I really love

mud!!!

CONDENSATION

• Change of phase from gas to liquid

• Warming process

• Exothermic = heat is released

• Steam burn is more damaging than a burn from boiling water

It is warm inside the shower room

after taking a bath because

condensation is a warming process.

PROBLEM SOLVING

1. How much energy does a refrigerator have to

remove from 1.5 kg water at 200C to make ice

at -120C? Lf =334x103 J/kg, Cice = 2100

J/kgC0

2. How much heat is needed to melt 16.5 kg of

silver that is initially at 200C? Melting pt of

silver = 960.80C Lf =88.3x103 J/kg

Csilver=234 J/kgC0

3. An ice cube tray of negligible mass

contains 0.350 kg of water at 180C . How

much heat must be removed to cool the

water at 00C and freeze it?

4. How much heat is required to convert 12.0

g ice at -100C to steam at 1000C? Lv =2256

x103 J/kg Csteam =2010 J/kgC0

5. An aluminum ice cube tray containing 800

g of water has reached 00 C. If the heat is

being removed from it at the rate of 15

cal/second, how long will it take for all

water to freeze? Lf = 80 cal/g

4. What must be the initial speed of the lead

bullet at a temperature of 250 C so that heat

developed when brought to rest will be

sufficient to melt it? Assume that all the

initial mechanical energy of the bullet is

converted to heat and that no heat flows

from the bullet to the surroundings. Lead’s

melting point is 327.30 C, Lf = 24.5 x 103 ,

C lead = 130 J/kgC0

5. A block of ice at its melting point and with

an initial mass of 50.0 kg slides along a

horizontal surface starting at a speed of 5.38

m/s and finally coming to rest after

travelling 28.3 m. Compute the mass of ice

melted as a result of friction between the

block and the surface. (Assume that all heat

generated owing to friction goes into the

block of ice)

SEATWORK

• How much heat must be released to convert

10.0 g steam at 1000C to ice at -50C? Lv =2256

x103 J/kg, Lf =334x103 J/kg, Csteam =2010

J/kgC0

• How much heat should be supplied to 50 g of

ice at -50 C in order to convert it to liquid at 250

C?

A 54.0 kg ice skater moving at 6.4 m/s glides

to a stop assuming the ice is at 00C and that

50% of heat generated by friction is absorbed

by the ice.=, how much ice melts?

. A pick up truck whose mass is 2200 kg is

speeding along the highway at 105 km/h. a) if

you could use all this kinetic energy to

vaporize water already at 1000 C, how much

water could you vaporize? Lv = 2256x 10 3

J/kg

At a crime scene, the forensic investigator

notes that the 8.2 g lead bullet that was

stopped in a door frame apparently melted

completely on impact. Assuming the bullet

was fired at room temperature (20 0 C) ,

what does the investigator calculate the

initial velocity of the gun was. Lead’s

melting point is 327.30 C, Lf = 24.5 x 103 ,

C lead = 130 J/kgC0

• Heat is transferred from hotter substance to colder substance upon contact with each other.

• Heat conduction occurs by electron and molecular collisions.

• Metals are good conductors of heat.

Conduction

• http://www.absorblearning.com/media/attachment.action?quick=aj&att=750

Particle to particle interaction

• Liquids and gases, are poor conductors.

• Air is a very poor conductor.

CONDUCTION

Does it feel so cold inside an

ice hotel?

No, it’s not that cold. Thanks to the poor heat

conductivity of ice

Snow is a poor conductor of heat.

Snow does not provide heat, it slows down the loss of heat they generate.

Insulating materials delay the transfer of heat.

Thanks to snow’s poor

heat conductivity!

In desert regions that are hot in the

daytime and cold at nightime, the walls of houses are often made of mud. Why is it important that the mud walls be

thick?

• Liquids and gases transmit heat by convection

• Heat transfer by actual motion of the fluid –by currents.

• Heat transfer in an empty space.

• Energy radiated is radiant energy.

Absorber and Emitter of radiation

• A perfect absorber reflects no radiant energy and appears perfectly black

• Good reflectors are poor absorbers

The skin pigmentation of chameleons allows it to modify its temperature. A chameleon will also make itself flat and dark so it can absorb more heat. The chameleon can turn a lighter color in an attempt to cool down.

Think…think…think…

• What color should you paint your house (light or dark colored) to stay cooler in summer. Why?

• Next time you go to a coffee shop,

when should you pour the creamer

on the coffee to maintain its hotness?

(immediately after receiving it or when

you are about to drink it)

• A tile floor may feel uncomfortably cold to your bare feet, but a carpeted floor in an adjoining room at the same temperature feels warm. Why?

Rate of heat flow through conduction

• H= rate of heat flow

• K= thermal conductivity

• TH = high temperature

• Tc = low temperature

• L = distance between two ends

• A =area perpendicular to thermal gradient

Problems:

• A major source of heat loss from a house is through windows. Calculate the rate of heat flow through a glass window 2.0 m x 1.5 m in area and 3.2 mm thick, if the temperature at the inner and outer surfaces are 15.00 C and 14.00 C respectively. Kglass = 0.84 W/mC0.

• Over what distance must there be heat flow by conduction from the blood capillaries beneath the skin to the surface if the temperature difference is 0.5 C0 . Assume 200 W must be transferred through the whole body’s surface area 1.5 m2 . K(human tissue) = 0.2 W/mC0 .

• Conduction through a picnic cooler. A styrofoam box used to keep drinks cold at a picnic has a total wall area of 0.80 m2 and wall thickness of 2.0 cm. It is filled with ice, water and cans of Coca cola at 00 C. What is the rate of heat flow into the box if temperature outside the wall is 300 C? How much ice melts in one day? Kstyrofoam = 0.01W/mC0

• A steel bar 10.0 cm long is welded end to end to a copper bar 20.0 m long. Both bars are perfectly insulated. Each bar has a square seciton 2.00 cm on a side. The free end is maintained at 1000 C, by placing it in contact with steam and free end of copper is maintained at 00 C, by placing it in contact with ice. Find the temperature at the junction of the two bars and the total rate of heat flow. Kcopper = 385.0 W/mK Ksteel = 50.2 W/m K .

Heat flow through radiation

• e = emissivity

• = Stefan Boltzmann constant = 5.67 x 10-8

W/m2 K4

• T1 = object’s temperature

• T2 = surrounding’s temperature

• An athlete is sitting unclothed in a locker room whose dark walls are at a temperature of 150

C. Estimate the rate of heat loss by radiation , assuming a skin temperature of 340C and e =0.70 if the surface area of the body is 1.5 m2

• If the total surface area of the human body is 1.20 m2 and the surface temperature is 300 C, find the total rate of radiation of energy from the body. If the surroundings are at a temperature of 250 C, what is the net rate of heat loss from the body by radiation? Emissivity is equal to 1.

EXERCISES

• A carpenter builds an outer house wall with a layer of wood 3.0 cm thick on the outside and a layer of styrofoam insulation 2.2 cm thick as the inside wall surface. The wood has k = 0.08 W/mC0 and the styrofoam has k = 0.010 W/mC0 . The interior surface temperature is 19.00 C and the exterior surface temperature is 280 C . A) What is the temperature at the plane where the wood meets the styrofoam

• A food container is surrounded by a styrofoamto keep it warm. The temperature inside the container is 50 0 C and the temperature outside is 25 0 C . What is the rate of heat transfer if the styrofoam has a total area of

0. 005 m2 and has a thickness of 2cm?

k styrofoam= 0.010 W/mC0

• One hot summer day, the surrounding temperature is 380 C, a glass wall having an area of 6m2 is fully covered by a styrofoaminsulation. The thickness of the glass wall and styrofoam is 10 cm and 7 cm respectively. What is the temperature at their junction if the temperature inside the house is 230 C? Kglass = 0.84 W/mC0 Kstyrofoam= 0.010 W/mC0

EXERCISES

• A thin square steel plate , 10 cm on a side, is heated to a temperature of 8000 C. If the emissivity is 0.60, what is the total rate of radiation of energy?