Physics/Y4/Temperature

Temperature
Let’s start things off by saying that heat and temperature are not the same thing. Although in everyday life, we can swap these two terms around quite a bit, physicists are really picky people. This is exactly why so many of them die alone, bitter and unloved in their 80s. Temperature is just a value that just so happens to be fixed to be directly proportional to the average kinetic energy of molecules within a substance. It is not the total kinetic energy. Heat on the other hand, is the total internal energy within a substance. It consists of not only the total internal kinetic energy present due to molecular movement but also the potential energy a substance possesses. Are we all clear on that? Good.

Two things can happen when you inject heat into a body, like when you put a kettle on a stove:

Its temperature can increase. The increased heat makes the molecules of the substance move around faster. This increases the overall kinetic energy, which is related (albeit not directly) to the molecules’ speed. This causes the mean kinetic energy in the heated body to increase. Since temperature is directly proportional to the mean kinetic energy, the temperature will increase, as governed by this equation: Q=mcΔT

Where Q is the gain in heat (measured in Joules) and m is the mass of the substance. The lower case ‘c’ is what is known as the specific heat capacity of the substance. This is defined as the amount of heat energy required to raise the temperature of 1kg of the substance by 1 Kelvin (to convert from degrees Celsius to Kelvin, add 273 to the Celsius reading). The ΔT refers to the change in temperature, in degrees Celsius or in Kelvins.

When the specific heat capacity or mass is unavailable, one can just use this equation:

$$Q = C{\vartriangle}T$$

Where the upper case ‘C‘ is the heat capacity of the substance, defined as the amount of heat energy to raise the temperature of an object by 1 Kelvin.

It can change state. As explained earlier, if the molecules gain enough energy, they can break out of intermolecular bonds holding them together. Because all the heat energy is used to change the bonding, there is no increase in temperature during this process. The change is in the internal potential energy and not in the kinetic energy that the measurement of temperature is tied to. The heat energy gained can be calculated using this formula:

$$Q = ml$$

Where ‘l‘ is the specific latent heat of fusion or vaporisation, depending on if you’re melting/freezing or boiling. Do note that unlike evaporation, the boiling of pure substances happens at a fixed temperature and happens throughout the liquid. However, this fixed temperature can be affect by pressure. For water, the lower the pressure, the lower the boiling point and vice versa.

Thermal equilibrium
When two bodies with different temperatures are in thermal contact in a closed system, they like to reach a state equilibrium, which is sort of like a state of thermal Zen, where both bodies experience no net loss or gain of energy between them. To calculate the equilibrium temperature, one must remember that since no energy is lost, all the energy lost by the hotter body will be gained by the cooler body. Here’s the formula:

$$\,\!m_1c_1(T_{1-i}-T_{1-f}) = m_2c_2(T_{2-f}-T_{2-i})$$

Where m1 is the mass of the hot body and m2 is the mass of the cold body. Likewise, c1 is the specific heat capacity of the hot body and c2 is the specific heat of the cold body. T1-i will be the initial temperature of the hot body and T1-f would be the final temperature of the hot body. T2-i would then be the initial temperature of the cold body while T2-f will be its final temperature.

Power and heat
Sometimes, you might be asked how much heat (Q, in Joules) is generated by a heater of power (P, in Watts) over a certain time period (t, in seconds). If this happens, just plug in this formula:

$$Q = P \times t$$

Measuring the temperature
The 0th Law of Thermodynamics (which seems terribly like an afterthought) states that:

If system A is in thermal equilibrium with system B which is in equilibrium with system C, system A is in thermal equilibrium with system C.

Imagine a thermometer as your system B. This is exactly how thermometers work: By getting into thermal equilibrium with the bodies it measures, the thermometer gives you a reading. It takes time to get to this equilibrium, which is why it is important to read only the first steady reading if one gives two hoots about experimental accuracy.

The most common type of thermometers in use are liquid-in-glass thermometers, which rely on the expansion of a certain liquid (most commonly mercury or alcohol) in response to changes in temperature. Take note that the liquid you use must have a greater rate of expansion than its glass container. Otherwise, the glass would expand faster than the liquid and you will be unable to see a rise in the liquid level. Many other physical properties that vary linearly (otherwise your thermometer will be hell to calibrate) can be used, like electrical resistance or the expansion rates of metals (see your bimetallic strip). Liquid-in-glass thermometers are just the most common. Here’s a side-by-side comparison of the advantages and disadvantages of the two most common thermometer liquids.