Thermal Energy

 

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)

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)?

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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).

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 đ?‘Źđ?’’đ?’–đ?’‚đ?’•đ?’Šđ?’?đ?’?: ∆đ??¸ = đ?‘šđ?‘?∆đ?œƒ E = Energy m = Mass c=Specific heat capacity đ?œƒ = Temperature

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?

đ??¸ = đ?‘„đ?‘‰ and đ??ź =

đ?‘„ đ?‘Ą

đ?‘Ź đ?‘„đ?‘‰ đ?‘„ đ?‘ƒ= = = đ?‘‰ = đ?‘°đ?‘˝ đ?’• đ?‘Ą đ?‘Ą From above equation‌ đ??¸ = đ??źđ?‘‰ đ?‘ đ?‘œ ‌ . đ??¸ = đ?‘‰đ??źđ?‘Ą đ?‘Ą ∆đ??¸ = đ?‘šđ?‘?∆đ?œƒ and ∆đ??¸ = đ?‘‰đ??źâˆ†đ?‘Ą Thus‌ đ?‘šđ?‘?∆đ?œƒ = đ?‘‰đ??źâˆ†đ?‘Ą đ?‘˝đ?‘°âˆ†đ?’• Rearranging: đ?’„ = đ?’Žâˆ†đ?œ˝

For example: Initial Temperature: 291 Kelvin Final Temperature: 319 Kelvin Time taken = 10 minutes = 600 s Voltage = 12 V I. With liquids‌ Current = 3.2 A Mass of block = 0.8 kg

đ?‘?= đ?‘?=

E = Energy Q = Charge V = Voltmeter I = Current m = mass ∆đ?œƒ = Change in temperature c = Specific heat capacity

đ?‘‰đ??źâˆ†đ?‘Ą đ?‘šâˆ†đ?œƒ 12 Ă— 3.2 Ă— 600 0.8 Ă— 319 − 291

đ?’„ ≈ đ?&#x;?đ?&#x;Žđ?&#x;?đ?&#x;— đ?‘ą đ?’Œđ?’ˆâˆ’đ?&#x;? đ?‘˛âˆ’đ?&#x;?

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:

=

∆ ∆

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.

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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.

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

of the molecules to the temperature on the Kelvin scale.

m đ?‘? k T đ?‘?

đ?&#x;? đ?&#x;‘ đ?’Ž đ?’„đ?&#x;? = đ?’Œđ?‘ť đ?&#x;? đ?&#x;? mass of one molecule (in kg) mean of speed-squared Boltzmann constant (1.38 x 10-23 J K-1) temperature (in Kelvin) 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 Ă— 0−27 đ?‘˜đ?‘” ) đ?‘˘

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

Calculation: đ?‘š

Average KE =

3

đ?‘?

= đ?‘˜đ?‘‡ =

3

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

Average kinetic energy = 6.0651 x 10-21 J đ?‘š đ?‘?

đ?‘?

= 6.0651 x 10-21 J =

6.065 Ă— 0−21 đ?‘š

r.m.s. speed =

đ?‘?

=

6.065 Ă— 0−21 3.3463608 x 0− 7

= 3.62489305 x 106

= 3.62489305 Ă— 106 = 1903.915189 ≈ 1904 đ?‘š/đ?‘

Conclusion: Average kinetic energy = 6.0651 x 10-21 J r.m.s. speed = 1904 m s-1

"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."

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 23

(1 mole = 6.02 x 10 molecules)

R T

Universal gas constant = 8.31 J K-1 mol-1 Temperature (in Kelvin Scale)

THE IDEAL GAS