Heating and Cooling of Water?

Question

1.How much energy needs to heat 1.5 L of water from 20 C to 100 C

2. 1.5 L water on cooking plate of 2.0 kW, takes 7 min to heat water from 20 to boiling, How much energy required? what is the eddiciency of heating process?

P.S. density of water is 1000 kg/m3 and specific heat capacity of water is 4.3 kJ/kg C.

Answer 1

All these questions can be answered using the formula:

E = mc(T2-T1)

For the first question, 1.5 L of water has a mass of 1.5 kg (1 cm^3 = 1 mL).

The energy needed to heat from 20 to 100 C would be:

E = 1.5kg(4.3 kJ/kg)(100-20C) = 516 kJ

This is the answer to question 1, but we will also need to remember this answer for question 2 as well.

We can calculate the total energy going into the cooking plate as we know the power and the time.

P=E/t or E = Pt

E = 2 kJ/s(7 min)(60s/min) = 840 kJ

This shows that we are putting 840 kJ into the cooking plate, but only getting 516 kJ transferred to the water.  Therefore the efficiency is:

n = Qout/Qin = 516 kJ/840 kJ = 0.614

Therefore, the efficiency of the heating process is only 61.4%.