HEAT AND TEMPERATURE

Key points

 Heat q is thermal energy transferred from a hotter system to a cooler system that are in contact.

 Temperature is a measure of the average kinetic energy of the atoms or molecules in the system.

 The zeroth law of thermodynamics says that no heat is transferred between two objects in thermal

equilibrium; therefore, they are the same temperature.

 We can calculate the heat released or absorbed using the specific heat capacity C, the mass of the

substance m, and the change in temperature ΔT, in the equation:

q=m×C×ΔT

Heat in thermodynamics

What contains more heat, a cup of coffee or a glass of iced tea? In chemistry class, that would be a trick

question (sorry!). In thermodynamics, heat has a very specific meaning that is different from how we

might use the word in everyday speech. Scientists define heat as thermal energy transferred between two

systems at different temperatures that come in contact. Heat is written with the symbol q or Q, and it has

units of Joules.

Heat is sometimes called a process quantity, because it is defined in the context of a process by which

energy can be transferred. We don't talk about a cup of coffee containing heat, but we can talk about the

heat transferred from the cup of hot coffee to your hand. Heat is also an extensive property, so the change

in temperature resulting from heat transferred to a system depends on how many molecules are in the

system.
 Calculating q using the heat capacity

We can use the heat capacity to determine the heat released or absorbed by a material using the following

formula:

q= m×C×ΔT

where m is the mass of the substance (in grams), C is the specific heat capacity, and ΔT is the change in

temperature during the heat transfer. Note that both mass and specific heat capacity can only have

positive values, so the sign of q will depend on the sign of ΔT. We can calculate ΔT using the following

equation:

ΔT=Tfinal−Tinitial

where Tfinal and Tinitial can have units of either. Based on this equation, if q is positive (energy of the

system increases), then our system increases in temperature and Tfinal > Tinitial. If q is negative (energy of

the system decreases), then our system's temperature decreases and Tfinal < Tinitial.

Differences between Heat and Temperature

In daily life most of us use these terms interchangeably. In this section we learn

differences between them.

1. Heat is a type of energy, but temperature is not energy.

2. Heat depends on mass of the substance, however; temperature does not depend on the
quantity of matter. For example, temperature of one glass of boiling water and one

teapot of boiling water are equal to each other; on the contrary they have different heat

since they have different masses.

3. You can measure temperature directly with a device called thermometer but heat

cannot be measured with a device directly. You should know the mass, temperature

and specific heat capacity of that matter.

4. If you give heat to a matter, you increase its temperature or change its phase.
Specific Heat Capacity

If you give same amount of heat

to different type of matters you

observe that changes in their

temperatures are different. For

instance, all you experience that

given an equal amount of heat to

metal spoons and wooden spoons,

metal spoon has greater change in

its temperature. Thus, most of the

housewives use wooden or plastic

spoons while cooking. These examples show that each matter has its own characteristics to absorb heat.

We call this concept as specific heat capacity of the matters. It is the distinguishing property of matters.

We show it with the letter “c” and give the definition of it as, heat required to increase temperature of unit

mass 1 ºC.On the contrary, heat capacity of the system is defined as “heat required increasing the

temperature of whole substance” and we show it with “C”.

C = m • c where m is the mass of the substance and c is the specific heat of the matter.

Temperature is measured using a variety of temperature scales. The most commonly used are described in

the next two sections.

1. The Celsius Scale (°C) This scale puts the freezing point of water at Oo C and the boiling point of

water at 100o C. The temperatures in between are divided up into 100 units (degrees).

• The disadvantages of this scale are:

• There may be temperatures below 0oC. The pressures and volumes of gases do not change in

proportion to Celsius temperature.

2. The Kelvin Scale (K) This scale has absolute zero as the zero point on it’s scale. The size of the

degree is the same as a Celsius degree. Advantages:

• Pressures and volumes of gases will change in proportion to Kelvin temperature. Absolute zero

is 273 degrees below 0oC. To convert from Celsius degrees to Kelvin degrees: add 273. To

convert from Kelvin degrees to Celsius degrees: subtract 273.

TRANSMISSION OF HEAT

Heat may be transferred from one place to another in three ways:

• Conduction

• Convection

• Radiation

• Direct Burning

a. Conduction is most obvious in solids. All liquids (except mercury) and gases are very poor

conductors of heat. When a solid heats up, its particles gain kinetic energy and increase the

energy with which they vibrate. Conduction occurs when heat energy travels through a body,

passing from particle to particle as they vibrate against each other. A good conductor must have

particles which are close enough together to collide with sufficient force for energy to be

transferred. Metals are all good conductors of heat especially copper, aluminium and silver,

because they have “free” electrons which are easily able to transfer heat energy.

b. Convection is the transfer of heat by the movement of the heated particles themselves. This can

only take place in liquids and gases because in solids the particles are not able to move from their

fixed positions. When a liquid or gas is heated, it expands and becomes less dense. The lighter

liquid or gas rises allowing a flow of cooler material to take its place. This in turn becomes heated

and so a current is set up. Heat will continue to be transferred through the available space in this

way until it is evenly distributed.

c. Radiation is the way we receive heat energy from the sun. It does not require a medium for its

transmission (i.e. it can travel through empty space) and is in the form of electromagnetic energy

waves which travel in the same way as light or radio waves. When these energy waves fall on a

body, the energy may be:

• transmitted

• reflected

When radiant energy is absorbed the body will rise in temperature. A rack of clothes left in front

of a radiant heater will continue to absorb heat until it reaches ignition temperature. Black and

dull surfaces absorb (and radiate) heat much more efficiently than white shiny surface The

amount of heat energy received decreases with the square of the distance from a radiant source,

for example, if an object is moved to twice the distance from a source, it will only receive a

quarter of the heat energy it would have received at the original distance. Radiant energy is

transmitted through clear materials such as glass. The glass does not heat up. Radiant heat from

the sun may be concentrated by means of a magnifying glass, sufficient to ignite flammable

material. Shiny, silver surfaces will reflect radiant energy and not heat up. This is the reason for

the silver coating on a fire-fighter’s jacket.

d. Direct Burning Some agencies use the term ‘direct burning’ to describe how physical contact of

the flame with other available fuel spreads a fire. By this form of direct fire spread, the heat of a

fire will transfer across any area where there is a line of fuel for the fire to follow. Some examples

of direct burning are:

SUMMARY

• Fire spreading along a piece of wood and setting fire to other pieces of wood that are in contact

with it.

• A candle places close enough to an object that the flame touches it.

Summary Heat and Temperature

• Heat is a form of energy.

• Heat is a measure of the total kinetic energy of the particles in a body

• Heat is measured in Joules (J) or kilojoules (kJ).

• Heat energy flows from bodies of high temperature to bodies of lower temperature.

• The heat content of a body depends on its mass, temperature and the material it is made of.
• Temperature is the degree of hotness.

• Temperature is a measure of the average kinetic energy of the particles in a body.

• At absolute zero, the particles have zero kinetic energy.

• If heat is put into a body, the temperature rises (unless a change of state is taking place).

• Temperature scales used are Celsius (o C) and Kelvin (K): K = o C + 273 o C = K – 273 Water

as an Extinguishing Agent

• Specific heat is the amount of heat required to raise the temperature of 1 kg of substance by 1o

C.

• The latent heat of vaporisation is the amount of heat required to change 1 kg of a substance from

a liquid to a gas or vapour.

• Water is a very effective cooling agent because of its high specific heat and high latent heat of

vaporisation.

• More heat is required to change water to steam than to raise its temperature to boiling point.

Transmission of Heat

• Heat is transferred by conduction, convection and radiation and direct burning.

• Conduction takes place in solids when the heat energy is transferred from particle to particle, by

collision.

• Metals are good conductors of heat

• Fire spread by conduction may take place along steel beams.

• Convection takes place in liquids and gases, when the substance itself moves, carrying the

energy with it.

• Fire spread may take place by convection when hot gases rise to the top of a building

• Replacement of hot gases by cooler ones when convection takes place means a fire may have a

continuous supply of oxygen.

• Radiation is the transfer of heat by energy waves.

• Radiant energy may be absorbed, transmitted, reflected

• Black, dull surfaces are good absorbers (and radiators).

• Transparent materials transmit radiant energy.

• Radiant energy decreases with the square of the distance from the source.

• Fire spread by radiation may take place when materials continue to absorb radiant energy until

ignition temperature is reached.

Examples

1. An 800-g silver gravy bowl is filled with hot gravy at 100ø C. If the silver bowl is originally at

room temperature (20oC), how much heat energy is required to warm the bowl up to the

temperature of the gravy? The specific heat of silver is 0.56 x 10-1 cal/g oC.

Q = 800 g x 0.056 cal/g- oC x (100 - 20) oC

Q = (64 x 103) (5.6 x 10-2 cal)

= 3.6 x 103 calories

2. Assume you have 250 cm3 of coffee in a cup of thermal capacity 20.0 cal / oC and and a silver

spoon of mass 80.0 g all at 80.0 oC. You desire to have your coffee at 45.0 oC for drinking. How

much water at 10.0 oC will you have to add? Assume coffee has the same specific heat as water.

heat energy lost = heat energy lost by coffee + heat energy lost by cup + heat energy lost by

spoon

HELcoffee = 250 cm3 x 1.00 g/cm3 x 1.00 cal/g x (80.0 -45.0)ø C

= 8750 cal

HELcup = 20.0 cal/ oC x (80 - 45) oC

= 700 cal

HELspoon = 80.0 g x 0.056 cal/g oC x (80.0 -45.0) oC

= 160 cal

heat energy gained = mw x 1 x (45.0 -10.0) oC = 35.0mw

35.0 mw = 9610 cal mw

= 275 g of water
3. What is the heat in joules required to raise the temperature of 25 grams of water from 0 degrees C
to 100 degrees C? What is the heat in calories?

Useful information: specific heat of water = 4.18 J/g·°C

Part I

Use the formula

q = mcΔT
where
q = heat energy
m = mass
c = specific heat
ΔT = change in temperature
q = (25 g)x(4.18 J/g·°C)[(100 C - 0 C)]
q = (25 g)x(4.18 J/g·°C)x(100 C)
q = 10450 J

Part II
4.18 J = 1 calorie
x calories = 10450 J x (1 cal/4.18 J)
x calories = 10450/4.18 calories
x calories = 2500 calories

Answer:
10450 J or 2500 calories of heat energy are required to raise the temperature of 25 grams of water
from 0 degrees C to 100 degrees C.

4. It takes 487.5 J to heat 25 grams of copper from 25 °C to 75 °C. What is the specific heat in
Joules/g·°C?

Solution:
Use the formula
q = mcΔT
where
q = heat energy
m = mass
c = specific heat
ΔT = change in temperature
Putting the numbers into the equation yields:

487.5 J = (25 g)c(75 °C - 25 °C)

Answer:
The specific heat of copper is 0.39 J/g·°C.

5. How much heat must be absorbed by 375 grams of water to raise its temperature by 25° C?

mw = 375 g

cw = 4.18 J/g·K

∆T = 25° C = 25 K

qg = mwcw∆Tw

qg = 375 g x 4.18 J/g·K x 25 K = 3.9 x 104 J