How to Calculate the Change in Temperature

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Thermodynamics is the field of physics concerned with temperature, heat and, ultimately, energy transfers. Although the laws of thermodynamics can be a little tricky to follow, the first law of thermodynamics is a simple relationship between the work done, heat added, and the change in internal energy of a substance. If you have to calculate a change in temperature, it’s either a simple process of subtracting the old temperature from the new one, or it may involve the first law, the amount of energy added as heat, and the specific heat capacity of the substance in question.

TL;DR (Too Long; Didn't Read)

A simple change in temperature is calculated by subtracting the final temperature from the initial temperature. You may need to convert from Fahrenheit to Celsius or vice-versa, which you can do using a formula or an online calculator.

When heat transfer is involved, use this formula: change in temperature = Q / cm to calculate the change in temperature from a specific amount of heat added. Q represents the heat added, c is the specific heat capacity of the substance you’re heating, and m is the mass of the substance you’re heating.

What’s the Difference Between Heat and Temperature?

The key bit of background you need for a temperature calculation is the difference between heat and temperature. The temperature of a substance is something you are familiar with from everyday life. It’s the quantity you measure with a thermometer. You also know that the boiling points and melting points of substances depend on their temperature. In reality, temperature is a measure of the internal energy a substance has, but that information isn’t important for working out the change in temperature.

Heat is a bit different. This is a term for the transfer of energy through thermal radiation. The first law of thermodynamics says that the change in energy equals the sum of the heat added and the work done. In other words, you can give more energy to something by warming it up (transferring heat to it) or by physically moving or stirring it (doing work on it).

Simple Change in Temperature Calculations

The simplest temperature calculation you may have to do involves working out the difference between a starting and finishing temperature. This is easy. You subtract the final temperature from the starting temperature to find the difference. So if something starts at 50 degrees Celsius and finishes at 75 degrees C, then the change in temperature is 75 degrees C – 50 degrees C = 25 degrees C. For decreases in temperature, the result is negative.

The biggest challenge for this type of calculation occurs when you need to do a temperature conversion. Both temperatures must be either Fahrenheit or Celsius. If you have one of each, convert one of them. To switch from Fahrenheit to Celsius, subtract 32 from the amount in Fahrenheit, multiply the result by 5, and then divide it by 9. To convert from Celsius to Fahrenheit, first multiply the amount by 9, then divide it by 5, and finally add 32 to the result. Alternatively, just use an online calculator.

Calculating Temperature Change From Heat Transfer

If you’re doing a more complicated problem involving heat transfer, calculating the change in temperature is more difficult. The formula you need is:

Change in temperature = Q / cm

Where Q is the heat added, c is the specific heat capacity of the substance, and m is the mass of the substance you’re heating up. The heat is given in joules (J), the specific heat capacity is an amount in joules per kilogram (or gram) °C, and the mass is in kilograms (kg) or grams (g). Water has a specific heat capacity of just under 4.2 J/g °C, so if you’re raising the temperature of 100 g of water using 4,200 J of heat, you get:

Change in temperature = 4200 J ÷ (4.2 J/g °C × 100 g) = 10 °C

The water increases in temperature by 10 degrees C. The only thing you need to remember is that you have to use consistent units for mass. If you have a specific heat capacity in J/g °C, then you need the mass of the substance in grams. If you have it in J/kg °C, then you need the mass of the substance in kilograms.

References

About the Author

Lee Johnson is a freelance writer and science enthusiast, with a passion for distilling complex concepts into simple, digestible language. He's written about science for several websites including eHow UK and WiseGeek, mainly covering physics and astronomy. He was also a science blogger for Elements Behavioral Health's blog network for five years. He studied physics at the Open University and graduated in 2018.

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