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Joule found that if he took a 100 kg mass, elevated it 4.2 meters in the air and then lowered it using his apparatus, that he could warm 1 kg of water by 1o Celsius. How much heat energy does it take to raise the temperature of the water by 1o Celsius?

Answer :

Edufirst

Answer:

  • 4,116 joule

Explanation:

Using the law of conservation of energy, assuming no energy losses, the heat energy required to raise the temperature of the water by 1ºC is equal to the change in the mechanical energy of the 100 kg mass. This is, all the mechanical energy is transformed into heat.

          [tex]Heat=\Delta \text{Mechanical Energy}[/tex]

The 100 kg elevated mass has only potential energy at start and zero mechanical energy at end. Thus, the change in the mechanical energy is equal to the change in potential energy, and it is equal to the initial potential energy:

        [tex]\text{Initial potential energy}=m\times g \times height\\\\\text{Initial potential energy}=100kg\times 9.8m/s^2 \times 4.2m=4,116Joule[/tex]

And that is the answer: 4,116 joule

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