Jump to: Thermal concepts 3.1 Modelling a gas 3.2 Topic 3 Problems

3.1 Thermal concepts

Solids, liquids and gases

Molecules are held together by intermolecular forces

Temperature

Temperature is a scalar quantity measured in ℃C (Celcius) or K (KelvinBase SI unit), using a termometer.

The energy will tend to pass from a hotter object to a colder object until they reach thermal equilibrium.

Extra content on heat transfer (not IB required)

Absolute Temperature

To find temperature in Kelvin from temperature in Celcius remember that:

\begin{equation} 0\ Kelvin=-273.15\ ℃ \end{equation}

Temperature of a body in Kelvin is directly proportional to the average Kinetic energy½mv2 per molecules in the body. Therefore, there cannot exist a temperature lower than 0 Kelvin.

Internal energy

Internal energy is the sum of Kinetic energyassociated with the random/translational rotational motions of molecules and Potential Energyassociated with forces between molecules.

Specific heat capacity

\begin{gather} Q=mc\Delta T\\ Q=heat\ energy,\ m=mass,\ c\equiv specific\ heat\ capacity,\ \Delta T=temperature\ change \notag\\ \notag \end{gather}

Table of specific heat capacities (Use Isobaric mass heat capacity)

Phase change

Change of phase Process Kinetic energy Potential energy
Solid to liquid Melting Unchanged Increases
Liquid to solid Freezing Unchanged Decreases
Liquid to gas Boiling Unchanged Increases
Gas to liquid Condensation Unchanged Decreases

Potential energy increases with temperature because:

1.At a higher temperature, more atoms/molecules are in excited electronic states.

2.At higher temperature, more molecules are in excited vibrational states.

3.At higher temperature, more molecules are in excited rotational states.

Boiling only occurs at boiling point throughout the liquid.

Evaporation happens at any temperature. The particles with highest KE evaporate, reducing average KE.

Specific latent heat

\begin{gather} \Delta Q=mL\\ Q=energy\ supplied\ to\ the\ object,\ m=mass,\ L=specific\ latent\ heat \notag\\ \notag \end{gather}

Specific latent heat for fusion: the amount of heat required to change 1kg of a substance from solid to liquid without change in temperature.

Specific laten heat for vaporization: the amount of heat required to change 1kg of a substance from liquid to gas without change in temperature.

3.2 Modelling a gas

Gas laws

Boyle's law
\begin{gather} V\varpropto \frac{1}{P}\\ Volume\ is\ inversely\ proportional\ to\ pressure \notag\\ V_{1} P_{1} =V_{2} P_{2} \notag\\ \notag \end{gather}
Charles' law
\begin{gather} V\varpropto T\\ Volume\ is\ directly\ proportional\ to\ temperature \notag\\ \frac{V_{1}}{T_{1}} =\frac{V_{2}}{T_{2}} \notag\\ \notag \end{gather}
Gay-Lussac's law
\begin{gather} P\varpropto T\\ Pressure\ is\ directly\ proportional\ to\ temperature \notag\\ \frac{P_{1}}{T_{1}} =\frac{P_{2}}{T_{2}} \notag\\ \notag \end{gather}
Avagadro's law
\begin{gather} V\varpropto n\\ \frac{V_{1}}{n_{1}} =\frac{V_{2}}{n_{2}} \notag\\ Volume\ is\ proportional\ to\ the\ number\ of\ molecules\ of\ gas\ ( moles) \notag\\ \notag \end{gather}
Combined gas law
\begin{gather} PV=nRT\\ P=pressure,\ V=volume,\ n=moles\ of\ gas,\ R=ideal\ gas\ constant \notag\\ T=temperature \notag\\ Where\ R=8.31 (J/mol/K) \notag \end{gather}
Gas laws video

Kinetic model of an ideal gas

Ideal gas assumptions:

1.The collisions between molecules are perfectly elastic.

2.The molecules are identical spheres.

3.The volume of molecules is negligible compared to the volume of the gas.

4.Molecules do not interact with each other.

Implications

Absolute temperature is directly proportional to the average KE and average speed of the molecules of an ideal gas.

Mole, molar mass, avagadro constant

Mole

SI measure of quantity of a “chemical entity,” such as atoms, electrons, or protons. It is defined as the amount of a substance that contains as many particles as there are atoms in 12 grams of pure carbon-12. So, 1 mol contains 6.022×1023 elementary entities of the substance.

Molar mass

The molar mass is the mass of a given chemical element or chemical compound (g) divided by the amount of substance (mol).

Real gas vs. ideal gas

There are forces between molecules in real gases.

The volume of molecules is not negligible compared to the volume of gas in real gases.

Real gases are more similar to ideal gases under high temperature and low pressure.

Topic 3 Problems

1. Which one of these is not an assumption made when modelling an ideal gas?

A. The volume of molecules is negligible compared to the volume of the gas.

B. There are no collisions between molecules

C. Molecules do not interact with each other

D. The molecules are identical spheres

2. Two objects are in thermal contact. State and explain which of the following quantities will determine the direction of the transfer of energy between these objects.

A. The temperature of each object.

B. The area of contact between the objects.

C. The specific heat capacity of each object.

D. The mass of each object.

3. The temperature of an ideal gas of pressure 200 kPa is increased from 27 °C to 54 °C at constant volume. Which is the best estimate for the new pressure of the gas?

A. 400 kPa

B. 220 kPa

C. 180 kPa

D. 100 kPa

4. The temperature of an ideal gas is doubled. The average speed of the molecules increases by a factor of:

A. √2

B. 2

C. 4

D. 2√2

5. What happens to Kinetic energy and Potential energy during melting?

A. KE increases and PE remains unchanged.

B. KE remains unchanged and PE decreases.

C. KE decreases and PE decreases.

D. KE remains unchanged and PE increases.

6. Calculate how much energy a freezer has to remove from 1.5kg of water at 20°C to make ice at -12°C. Specific heat of ice is 2100 J/kg °C

A. 3.33x105J

B. 4.8x103J

C. 6.6x105J

D. 1.4x103J

7. The Kelvin temperature of an object is a measure of

A. the total energy of the molecules of the object.

B. the total kinetic energy of the molecules of the object.

C. the maximum energy of the molecules of the object.

D. the average kinetic energy of the molecules of the object.

Number of correct answers: