Question

Assume Lake Ontario contains 1.60 ✕ 10¹² m³ of water, and assume the water's density is that of water at 20°C and 1 atm. (a) How much energy (in J) is required to raise the temperature of that volume of water from 18.0 degree C to 25.6 degree C? (b) How many years would it take to supply this amount of energy by using a power of 1,400 MW generated by and electric power plant? (in yr)

Answer 1

Given data

i) volume of water is $V=1.60 \times 1012\textup{ m}^3=1619.2\textup{ m}^3$

ii) Initial temperature of water is $T_i=18^{\circ}\textup{C}=291\textup{ K}$

iii) Final required temperature of water is $T_f=25.6^{\circ}\textup{C}=298.6\textup{ K}$

At 20⁰C and 1 atm,

i) density of water is $\rho=1000\textup{ kg/m}^3$ and

ii) specific heat at constant pressure is $c_p=4.2\textup{ kJ/kg.K}$

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a)

The amount of heat required for this process is

$Q=m c_p (T_f-T_i)=\rho \times V \times c_p (T_f-T_i)$

$\Rightarrow Q=1000 \times 1619.2 \times 4.2 (298.6-291)$

$\Rightarrow Q=51684864\textup{ kJ}$

Therefore, $51684864 \times 10^3\textup{ J}$ of heat is required for the process.

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b)

Capacity of power supply is $P=1400\textup{ MW}=1400 \times 10^3 \textup{ kJ/s}$

Let t be the time taken for the plant to supply 10.88 GJ of energy. Then

  $Q=P \times t$

  $51684864 \times 10^3=1400 \times 10^6 \times t$

  $\Rightarrow t=36.92\textup{ sec}$

Converting sec into year, $\Rightarrow t=1.17 \times 10^{-6}\textup{ years}$