Question

how much water is needed to produce 1kwh of electricity at a power plant that is 30% efficient if the temperature increase 10 C

Answer 1

The amount of water needed is 287 kg

Explanation:

The amount of energy that we need to produce with the power plant is

$E=1 kWh = (1000W)(1h)=(1000W)(3600s)=3.6\cdot 10^6 J$

We also know that the power plant is only 30% efficient, so the energy produced in input must be:

$E_{in}=\frac{E}{0.30}=\frac{3.6\cdot 10^6}{0.3}=1.2\cdot 10^7 J$

The amount of water that is needed to produce this energy can be found using the equation

$E_{in}=mC\Delta T$

where:

m is the amount of water

$C=4186 J/kg^{\circ}C$ is the specific heat capacity of water

$\Delta T=10^{\circ}C$ is the increase in temperature

And solving for m, we find:

$m=\frac{E_{in}}{C\Delta T}=\frac{1.2\cdot 10^7}{(4186)(10)}=287 kg$

Learn more about specific heat capacity:

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