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?

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.

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:

And that is the 4,116 joule

1. for the first question, we must find the mass of the anhydrous salt, mgso₄. the molar mass for mgso₄·7h₂o is 246.47 g/mol, while that of mgso₄ is 120.37 g/mol.7.834 g mgso₄·7h₂o * 1 mol mgso₄·7h₂o/246.47 g * 1 mol mgso₄/1 mol mgso₄·7h₂o * 20.37 g mgso₄/mol = 0.647 g mgso₄

2. mass of water = mass of sample - mass of anhydrous salemass of water = 7.834 - 0.647 = 7.19 gpercent water in hydrate = 7.19/7.834 * 100 = 91.74%