Temperature and Heat

Two systems of temperature

Temperature conversions

Real science (one scale to rule them all)

The Kelvin Scale.

The Kelvin scale is similar to the Celsius Scale in that there are 100 divisions between the ice point and the boiling point of water.

Temperature scales

Effects of temperature on materials

Linear Thermal Expansion

The length, $L_0$, of a solid changes by an amount $\Delta L$ when its temperature changes by $\Delta T$.

where $\alpha$ is the coefficient of linear expansion.

The coefficient $\alpha$ is good to know when designing structures or devices with more than one material.

Examples of linear thermal expansion

$$\Delta L = \alpha L_0 \Delta T$$

The Bimetallic strip

If two metals, like brass and steel and joined together into a thin sheet like so, then when heated, since the $\alpha$ values are different for each metal, there will be significant bending of the strip.

$\alpha_\textrm{steel} = 12 \times 10^{-6}$

$\alpha_\textrm{brass} = 19 \times 10^{-6}$

Volume Thermal Expansions

The volume, $V_0$, of a solid changes by an amount $\Delta V$ when its temperature changes by $\Delta T$.

Heat and Energy

Energy, again

Previously, we waved away the effects of 'heat'.

We said that energy was lost due to heat, and other such things.

We could account for the lost energy, but that was about the extent of our dealings.

Heat: The flow of thermal energy from an object of higher temperature to an object of lower temperature.

SI unit: Joule

Let's say we want to change the temperature of an object by an amount $\Delta T$.

We'll need to transfer some amount of heat, $Q$, to the object in order to make this happen.

This amount will depend on the mass, $m$, of the object as well as the physical makeup of the object.

Here, $c$, is the Specific Heat .

Specific Heat

The specific heat of various materials is listed here.

(all at 25ºC and 1 atm)

Compare the effects of 10000 J of heat on 1 kg of sand vs 1 kg of water.

Phase Changes

Transitions

Transitions

The processes during which the ice melts is a constant temperature process.

Latent Heat

The Latent Heat of a material tells us how much heat is needed to undergo a phase transition.

For example, the Latent Heat of Vaporization, $L_V$, for water is $22.6 \times 10^5$ J/kg.

Thus, to boil away 1 kg of water (~ 1 L) we would need to apply 2 260 000 J of heat

Latent Heat of Fusion

Each type of phase transition requires its own Latent Heat Value.

The latent heat of fusion refers to the transition from a solid to a liquid.

Latent Heat of Vaporization

This value tells us how much heat is required to go from the liquid to the gas phase

The length of the plateaus in this graph are indicative of the various latent heat values.

Boiling, and vapor pressure

At the boundary between a liquid and a vapor, some of the constituent molecules will be migrating back and forth between the two phases.

In a closed container, when the same number of particles are leaving the fluid as are leaving the vapor, the vapor will be at a certain pressure. This pressure is called the equilibrium vapor pressure.

Heating the fluid will increase this vapor pressure.

The vapor pressure will be proportional to the temperature: higher temperature, higher vapor pressure.

Vapor pressure as a function of temperature.

Now we take a container open to the atmosphere.

If the vapor pressure is larger than the atmospheric pressure, then we will have unrestrained transformation from liquid to vapor i.e. boiling.

If the pressure inside a bubble is less than the pressure outside the bubble, the bubble will collapse.

If however, the pressure inside is greater than the pressure outside, then the bubble will survive!

This is boiling.

Boiling is the unrestrained conversion of the liquid to a gas (vapor). Thus, a liquid will boil when the external pressure is equal to the vapor pressure at the given temperature.

For example, we expect water to boil at 100 C, which is when the vapor pressure equals atmospheric pressure.

On a high mountain however, where the atmospheric pressure is less, then the boiling temperature is also less.

The Transfer of Heat

Now let's ask how heat is transferred.

Essentially, there are several ways we can move this motion around.

If heat is applied to a set of molecules, their thermal motion will increase.

This means that there will be tendency to increase the volume of the space they fill.

Since density is given by $\rho = m/V $, if the volume goes up, the density will go down.

Thus, heating a material will reduce the density.

Archimedes Principle

If a region of a fluid is less dense than the rest, there will be a buoyancy force on the less dense region, and that region of less dense matter will rise compared to the other parts.

Convection

The Movement of heat via the motion of a fluid

Convection Cells

In certain situations, this flow of heat can lead to the formation of convection cells.

Here, the convection current creates a cyclical behavior in the material.

Convection Cells

Conduction

Conduction

The amount of heat we transfer should be dependent on the following:

1. The Area of the connection. The larger $A$, the more heat can flow. ($Q \propto A$)
2. The length of the connection. The larger $L$, the less heat will flow in a given time.
3. The difference in temperature of the two objects.($Q \propto \Delta T$)
4. Some constant which describes the material. ($Q \propto k$)

Indeed, we can express the amount of heat flow by the following:

Some Thermal Conductivities

Radiation

Convection and Conduction required a medium between two bodies in order for heat to flow.

However, objects can transmit energy in the form of electromagnetic waves.

The sun for example, emits EM waves and these waves transfer the energy of the sun to the earth.

There is no medium in outer space. But the waves don't need a medium...