# Temperature

## Thermal Equilibrium

When two objects are in thermal equilibrium with each other, they will not exchange energy if placed in thermal contact. Thermal contact means that the objects are able to transfer energy to each other by conduction or electromagnetic radiation.

Example: Two blocks are placed in an empty, insulated container. The blocks are not touching, and so cannot transfer energy by conduction. The blocks can transfer energy by electromagnetic radiation, though, so they are in thermal contact (heat is often transmitted as infrared radiation). If the two blocks are in thermal equilibrium, there will be no energy transfer between them. If they are not in equilibrium, however, the hotter block will radiate energy to the colder one.

### 0th Law of Thermodynamics

If two bodies (A and B) are in thermal equilibrium with a third object (C), then A and B are in thermal equilibrium with each other.

## Temperature

Two objects are at the same temperature if they are in thermal equilibrium with one another. If two objects are not at the same temperature, they are not in thermal equilibrium and will transfer energy between each other. This means that temperature can be used to determine whether or not objects will transfer energy when placed in thermal contact.

Note: When we touch two objects at the same temperature, one may feel hotter than the other. This is because the way we sense heat depends on the rate of energy transfer between our skin and the object we are touching. Thermally conductive materials transfer energy more rapidly, and so will seem to be at more "extreme" temperatures. For example, a cold metal bottle feels very cold to touch, but a roll of fabric at the same temperature will only feel cool. The metal is a good thermal conductor, but the fabric insulates.

## Absolute Zero

Absolute zero is the lowest possible temperature. At this point, gas particles will cease to move, as they have no energy. In reality, it is impossible to reach absolute zero, but scientists have reached temperatures under one nanokelvin, which is extremely close.

Absolute zero is the base temperature on the absolute temperature scale, which is measured in Kelvin. One degree in Kelvin is the same size as one degree in Celsius. The Celsius temperature of absolute zero is -273.15oC, so to convert between Kelvin and Celsius, use the following equation:

TC = TK -273.15

Most equations require the temperature in Kelvin. If an equation requires a change in temperature (ΔT), then Celsius or Kelvin will both work, since degrees are the same size on both scales.

You will not need to convert to Farenheit in this course.

Note: The Celsius scale is defined by the properties of water at atmospheric pressure. When water and ice are in thermal equilibrium at atmospheric pressure (ice point), this is 0oC. 100oC is when steam and water are in thermal equilibrium at atmospheric pressure (steam point).

## Measuring Temperature

All temperature measuring devices rely on a system whose physical properties change with a conductor. Some common physical properties which can change with temperature include colour, liquid volume, gas pressure, electrical conductivity or dimensions of a solid.

### Thermometers

Liquid thermometers are one of the more common methods of measuring temperature - these rely on thermal expansion. A thermometer consists of a glass capillary tube with a bulb of fluid at the base, and calibrated temperature markings along the side.

Using a thermometer: The bulb of the thermometer is placed in thermal contact with an object. As the temperature increases, the thermometer fluid expands and so rises up the tube (decreasing temperature has the opposite effect). After some time, the thermometer fluid and the object come into thermal equilibrium and the fluid stops expanding. The temperature is then read off using the calibrated temperature markings.

Calibration: The thermometer is calibrated by marking the fluid height at the ice point (0oC) and steam point (100oC) of water. The space between these markings is then divided into 100 equal segments, each representing 1oC.

Problems: Thermometers of this type are not particularly accurate, as they assume that fluid expansion varies linearly with temperature. This means that thermometers are inaccurate at temperatures far from the calibration points. In addition, thermometers can only measure a limited range of temperatures, because the fluid inside may freeze or boil. Gas thermometers are less affected by the properties of the substance inside the thermometer, and so are a better choice than ordinary liquid thermometers.

## Thermal Expansion

Thermal expansion is when an object's size increases with temperature.

• In a solid, the dimensions of the object will increase.
• Liquid substances increase in volume.
• Gases at fixed pressure will increase in volume, while gases at fixed volume will increase in pressure.

To understand the cause for thermal expansion, imagine that the atoms in a solid are linked together by springs. Thermal energy in the solid causes the atoms to vibrate. As the thermal energy of the solid increases (due to heating), the atoms vibrate more and the average distance between them increases. Overall, this causes the solid to expand. For small temperature changes, the expansion is linearly related to the change in temperature.

Thermal expansion must be accounted for in construction and manufacture, to ensure that objects will not break due to varying temperature. For example, bridges have special joints which allow them to expand and contract a little. Otherwise, the bridge would buckle and break on hot days (or crack on cold ones).

### Thermal expansion equations

Change in length: The change in length (ΔL) is the proportional to initial length (Li) and the change in temperature (ΔT). The constant of proportionality is the thermal expansion coefficient (α), which is a property of the material which is expanding (or contracting).

ΔL = αLiΔT

Note that if temperature decreases, ΔT and ΔL will both be negative, as the object contracts.

Change in volume: By considering the change in length in 3 dimensions, the relationship for change in volume (below) may be produced. This equation is similar to that for change in length: the change in volume (ΔV) is proportional to initial volume (Vi) and change in temperature (ΔT). The constant of proportionality is now the volumetric expansion coeffiecient (β).

ΔV = βViΔT

The volume expansion formula may be applied to liquids as well as solids. β for liquids is generally ten times greater than for solids.

Applying the expansion equations: It is not always clear how an object will expand when heated. For instance, a disc with a hole at the centre will increase its outer radius, but it is unclear what happens to the inner radius. In circumstances like these, remember that it is the space between atoms which increases. Draw a simplified diagram and determine how the atoms will move when they separate. This should indicate how the object will change when heated. From the diagram below, we see that both the outer and inner radii increase under heating.

## End

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