Heat (or thermal energy) is a form of energy which transfers from a body or region of high

temperature to one of lower temperature.

Internal energy is the sum of kinetic energy of the molecules within a body and the potential

energy of the bonds between them.

Temperature is the average kinetic energy of the molecules, which is

measured in Kelvin (K), degree Celsius (°C), or degree Fahrenheit (°F)

Specific Heat Capacity is the energy transferred needed to change the temperature of 1 kg

substance by 1 Kelvin (units in J kg-1 K-1).

𝑬𝒒𝒖𝒂𝒕𝒊𝒐𝒏: ∆𝐸 = 𝑚𝑐∆𝜃

Same amount of heat energy transferred to two different objects will

increase their internal energy by the same amount. However, this will not

necessarily cause the same rise in temperature.

Factors affecting rise in temperature:

Amount of heat energy transferred

Mass of the object

Specific heat capacity of the material from which the object is

made

E = Energy m = Mass c=Specific heat capacity 𝜃 = Temperature

Kinetic theory states…

When energy is supplied to an object,

the particles in that object take up that

energy as kinetic energy – in solids, as

vibrations; in gas and liquids, as

whizzing molecules

Absolute Zero is…

The lowest temperature which is the

point when the substance has zero

thermal energy (at 0 Kelvin)

Exercise:

1. How many degree Celsius and degree

Fahrenheit in 0 Kelvin?

2. How many Kelvin and degree

Fahrenheit in room temperature (25

degree Celsius)?

The initial temperature of the block was measured and the supply was connected to the power

source.

After some minutes (say 10 minutes), the

power source was disconnected and the

final temperature was recorded.

What is the Specific Heat Capacity?

I. With liquids…

The process, variables, and calculations on this

are very similar to finding the specific heat

capacity of a solid block.

Measure initial temperature; heat up; measure

final temperature and time taken; then use:

= ∆

∆

𝑃 = 𝑬

𝒕=𝑄𝑉

𝑡=

𝑄

𝑡 𝑉 = 𝑰𝑽

𝐸

𝑡= 𝐼𝑉 𝑠𝑜… . 𝐸 = 𝑉𝐼𝑡

𝐸 = 𝑄𝑉 and 𝐼 =𝑄

𝑡

From above equation…

∆𝐸 = 𝑚𝑐∆𝜃 and ∆𝐸 = 𝑉𝐼∆𝑡

Thus… 𝑚𝑐∆𝜃 = 𝑉𝐼∆𝑡

Rearranging: 𝒄 = 𝑽𝑰∆𝒕

𝒎∆𝜽

E = Energy

Q = Charge

V = Voltmeter

I = Current

m = mass

∆𝜃 = Change in

temperature

c = Specific heat

capacity

For example:

Initial Temperature: 291 Kelvin

Final Temperature: 319 Kelvin

Time taken = 10 minutes = 600 s

Voltage = 12 V

Current = 3.2 A

Mass of block = 0.8 kg

𝑐 = 𝑉𝐼∆𝑡

𝑚∆𝜃

𝑐 = 12 × 3.2 × 600

0.8 × 319 − 291

𝒄 ≈ 𝟏𝟎𝟐𝟗 𝑱 𝒌𝒈−𝟏 𝑲−𝟏

When molecules collide, there is an exchange of energy. When a

molecule with more kinetic energy collides with one with less, they share the

energy evenly. The faster one slows down and the slower one speeds up. The

effect of those

collisions is that the

increase in kinetic

energy caused by heating becomes distributed

throughout the substance, with the heat

passing from hotter areas to colder areas.

Maxwell-Boltzmann Distribution is a graph that shows the distribution of the kinetic

energies of a collection of molecules at a particular temperature. This distribution can also

be used to compare the kinetic energies of a two or more collection of molecules with

different temperatures.

Molecular Kinetic Energy Equation – this equation relates the average kinetic energy

. .=

of the molecules to the temperature on the Kelvin scale.

𝟏

𝟐𝒎 𝒄𝟐 =

𝟑

𝟐𝒌𝑻

m mass of one molecule (in kg)

𝑐 mean of speed-squared

k Boltzmann constant (1.38 x 10-23 J K-1)

T temperature (in Kelvin)

𝑐 root-mean-square speed

Question:

Find the average kinetic energy and the r.m.s. speed of hydrogen gas, H2, molecules in a Zeppelin

aircraft at 20°C?

(Atomic mass of hydrogen molecule = 2.01588 u)

Given:

T = 20°C = 20 + 273 K = 293 K (temperature must be in Kelvin)

m = 2.01588 u ( .66 × 0−27 𝑘𝑔

𝑢) = 3.3463608 x 10-27 kg (mass must be in kg)

Calculation:

Average KE =

𝑚 𝑐 =

3

𝑘𝑇 =

3

1.38 x 10-23)(293) = 6.0651 x 10-21 J

Average kinetic energy = 6.0651 x 10-21 J

𝑚 𝑐 = 6.0651 x 10-21 J

𝑐 = 6.065 × 0−21

𝑚 =

6.065 × 0−21

3.3463608 x 0− 7 = 3.62489305 x 106

r.m.s. speed = 𝑐 = 3.62489305 × 106 = 1903.915189 ≈ 1904 𝑚/𝑠

Conclusion:

Average kinetic energy = 6.0651 x 10-21 J

r.m.s. speed = 1904 m s-1

These all combine to form the ideal gas equation:

= =

Where:

p Pressure

V Volume

N Number of molecules

k Boltzmann’s constant = 1.38 x 10-23

N Number of moles (1 mole = 6.02 x 10

23 molecules)

R Universal gas constant = 8.31 J K-1 mol-1

T Temperature (in Kelvin Scale)

THE IDEAL GAS

"For constant mass and temperature, pressure

exerted by gas is inversely proportional to the volume it

occupies."

"For constant mass and pressure, the volume occupied by the gas is

proportional to its absolute temperature."

"For constant mass and volume, the pressure exerted by the gas is proportional to its absolute temperature."