Thermal Capacity

Physics - Thermal capacity

 Thermal capacity is how much heat is required to raise the temperature of a body by 1℃.

It's measured in joules per ℃, J/℃.

Equation

thermal capacity = mass × specific heat capacity 

or thermal capacity = m × c

Note: c is the symbol for specific heat capacity

Thermometers

Physics - Thermometers: liquid-in-glass

Key Terms:

Capillary tube - A glass tube with thick walls and a narrow interior hollow tube (bore). It has a bulb at one end. 

Image source and credit: http://www.advancedaquarist.com

To the left is a labelled diagram of a thermometer, you don't need to know all of the different parts of a thermometer, but I included it to help you understand.














How they work:

When the glass bulb is is heated, the liquid in the bulb starts to expand up the capillary tube. 

The liquid must have the following properties:

• Be able to be seen easily
• Be able to expand and contract quickly over a wide range of temperatures
• Not stick to the inside of the capillary tube

Commonly Mercury and Alcohol (coloured) are used because Mercury boils at 357℃ and freezes at -39℃. Alcohol boils at 78℃ and freezes at -115℃, therefore Alcohol is more suited to low temperatures and Mercury is suitable for higher temperatures.

Clinical Thermometers

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Clinical thermometers are used by doctors and nurses to measure patient's body temperatures, they are mercury-in-glass thermometers. 

These are different from normal mercury-in-glass thermometers as their scale only extends for a few degrees either side of 37℃, this is because 37℃ is the normal body temperature. 

The capillary tube in these thermometers is very narrow, allowing for a very accurate reading to be taken, a.k.a the thermometer has a high sensitivity.

How they work:

The capillary tube has a constriction (check diagram above if you don't know what this is) just above bulb.

The thermometer is placed under the tongue and kept there for 1 minute, the mercury expands it heats up and forces past the constriction. Once the thermometer is removed from the mouth, the mercury in the bulb cools and contracts, breaking off from the mercury thread at the constriction, but the mercury that's beyond the constriction stays in the tube, showing the body temperature is at. 

By flicking your wrist, the mercury returns to the bulb again.

Mercury thermometers (for clinical use) are now being replaced by digital thermometers, because mercury is toxic.



Thermocouple Thermometers

Thermocouples are used to measure temperatures that change quickly or are very high.

Thermocouple thermometers have wires made of two different materials, e.g iron and copper that are joined together. If one junction is at a higher temperature than the other one, an electric current flows, producing a reading on a digital voltmeter, the voltage of the current is directly related to the temperature.

They are used in industry to measure a vast range of temperatures from -250℃ to 1500℃, they are also very good at measuring the temperatures on small objects or for rapidly changing temperatures.



Resistance Thermometers

Resistance thermometers are used to measure temperatures accurately from -200℃ to 1200℃.
They work by using the fact that electrical resistance builds up in a platinum wire when the temperature increases. 
They are best used for steady temperatures and are bulky.


Constant-Volume Gas Thermometers

Constant-Volume Gas thermometers use the change in pressure of a gas to measure temperature. 
It works over a wide rang of temperatures, and is bulky.


Thermistors

Thermistors work over a small range, ie. -5℃ to 70℃. It's resistance decreases with temperature.

Thermochromic Liquids

Thermochromic liquids change colour when heated or cooled, they have a limited range of temperatures (around room temperatures).

Linear Expansivity

Definition

Linear expansivity is the increase of 1m of material in size for a 1℃ rise in temperature.

When designing bridges, railway tracks and copper piping etc. engineers have to allow for linear expansivity.

Linear expansivity is the amount by which a material increases in size due to an increase in temperature. It's measured in meters per degree Celsius. It's symbol is the greek symbol for alpha, α.

To calculate the linear expansion of something, you need to know the following:

• The length of the bridge
• The range of temperatures it will experience
• The linear expansivity of the material that's going to be used

The linear expansivity of materials is found through experimenting. 

Steel's linear expansivity is 0.000 012m per ℃, so 1m will become 1.000 012m if the temperature increases by 1℃.

Equation

expansion = linear expansivity ⨉ original length ⨉ temperature rise 

Example question and working

Question: How long will a 100m long steel  bridge become if the temperature increases by 60℃? Note that the linear expansivity of steel is 0.000 012m.

Answer: The bridge would expand by 0.000 012m ⨉ 100m if the temperature rose by 1℃. So if the temperature rises by 60℃, then the bridge would expand by 

0.000 012m ⨉ 100m ⨉ 60℃ = 0.072m or 7.2cm

Change in length 

Delta (the greek letter) often means the change in a quantity or the difference. So the change in temperature in the above question is 60℃ and the change in length is 7.2cm.

You need to remember the following symbols:

Delta: 

Change in length:

 Change in temperature:

Boyle's Law

You might think that Boyle's law is complicated, but it really isn't!

Boyle's law states: The pressure and volume of a gas have an inverse relationship, when temperature is held constant.

This means that if you take a container filled with a gas, and halve the size of the container, then the pressure will be doubled (because there will be twice as many collisions per second).