Question

Lake Erie contains roughly 4.20E+11 m³ of water. How much heat is required to raise the temperature of that volume of water from 10.7^oC to 13.0^oC?

How many years would it take to supply this amount of heat by using the full output of a 1160 MW electric power plant? Do not enter unit.

Answer 1

The heat required is given by the relation

m = mass = density x volume

density of water = 997 kg/m³

volume = 4.2 x 10¹¹ m³

m = 4.1874 x 10¹⁴ kg

c = specific heat of water = 4.186 J/g^oC

Change in temperature = 13- 10.7^oC = 2.3 ^oC

So, = 4.1874 x 10¹⁴ x 4.186 x 2.3 J = 4.03 x 10¹⁵ J

Hence Heat required = 4.03 x 10¹⁵ J

Power supplied = 1160 MW = 1160 x 10⁶ W

Power = Heat/Time required

Time required = 4.03 x 10¹⁵/ 1160 x 10⁶ = 3474138 s

One year = 365 days = 365 x 24 x 3600 s = 31536000 s

So, time in terms of year = 3474138/31536000 years = 0.11 years

So,

answer without units as mentioned in question

Heat required in terms of J = 4.03 x 10¹⁵

Time required in terms of year = 0.11