How much energy is needed to heat enough water to make up a cup of tea (250 mL), if the water is at 20 degrees Celsius and you want to increase the temperature to 85 degrees Celsius (assume that 1.00 ml of water has a mass of 1.00g.)
The specific heat of a substance is the amount of heat required to increase the temperature of a unit mass of a substance by 1 degree Celsius. In case of water, the specific heat is 4.186 J/gm/degree Celsius.
Since, there is no phase change (ice to water or water to vapor), only the specific heat is required for our calculations. In case of phase change, we would have needed latent energy as well.
Here, we have to heat enough water to make a cup of tea or 250 ml of tea. Given the specific gravity of water as 1, in other words, 1 ml of water has a mass of 1 gm. That is, we need to heat 250 gm of water. Also, the water is initially at 20 degree Celsius and has to be heated to 85 degree Celsius.
The amount of heat required = quantity of water x specific heat x change in temperature
= 250 gm x 4.186 J/gm/degree Celsius x (85-20) degree Celsius
= 68,022.5 J = 68.022 KJ
Thus, we need about 68 KJ of energy to heat enough water to make a cup of tea.
Hope this helps.