The amount of heat energy required to raise the temperature of a substance can be calculated as:
Q=m×c×∆Twhere
Q is the heat energy required,
m is the mass of the substance,
c is its specific heat capacity, and
∆T is the change in temperature.
The time required to heat a substance can be calculated as :
t=‌where
t is the time required, and
P is the power of the heating device.
The actual power output of the heating device can be calculated as:
P‌actual ‌=P‌input ‌×‌ efficiency ‌where
P−input is the input power to the device and efficiency is the fraction of input power that is actually converted to useful power output.
Substituting the given values:
Q=2‌kg×4200J∕kg∕K×(60−10)=2‌kg×4200J∕kg∕K×50K=4200×50×2J=420,000J P‌input ‌=2000W=2000J∕ sP‌actual ‌=2000×0.7=1400J∕ st=‌=‌J∕ s=300 sSo, the time required to heat
2‌kg of water from
10∘C to
60∘C is approximately
300 s.