Question

Lake Erie contains roughly 4.00 ✕ 10¹¹ m³ of water.

(a) How much energy is required to raise the temperature of that volume of water from 15.4°C to 22.6°C? (Assume the density of this water to be equal to that of water at 20°C and 1 atm.)
J

(b) How many years would it take to supply this amount of energy by using the 1,400-MW exhaust energy of an electric power plant?
yr

Answer 1

a) volume,V = 4*10¹¹ m³

Q = energy required = ?

T1= 15.4 C

T2 = 22.6 C

p= density = 10³ kg/m³

m= p*V

= 10³* 4*10¹¹ = 4*10¹⁴ kg

c= specific heat = 4.18*10³ J/Kg ⁰C

Q = m*c*(T2-T1)

Q = 4*10¹⁴*4.18*10³* ( 22.6 - 15.4)

Q = 1.20*10¹⁹ J

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b) T = time required =?

power = 1400 MW

P = energy/time

time = energy / power

time = 1.20*10¹⁹ J / 1400*10⁶ J/s ( 1W = 1J/s)

= 8.59*10⁹ s

=  8.59*10⁹ s / 365*24*60*60 s/yr

= 272.38 yr