Question

A 75 W light bulb is used for 9 hours a day. The electricity for this bulb comes from a natural gas fired power plant that operates with 46% efficiency. How much CO₂ is emitted per day to power this light bulb? Make a simple estimate of the CO2 emissions from the power plant, ignoring transmission losses.

Answer 1

In the question here it is asked to find the value of Carbon dioxide gas emitted in a day to power the light bulb of 75 Watts which runs for 9 hours. Let's solve the problem in steps and find the answer.

We first find the total energy in KWh needed by the bulb in one year =

75 X 9 X 365 = 246.375KWh 1000

Thermal energy content of natural gas

But the plant runs with 45% efficiency, hence the thermal energy content of the plant is = $= 13,859.8\times 0.45 KWh/ton = 6236.91 KWh/ton$

1 ton = 907.185 Kg

Therefore, the thermal energy content of the plant in KWh/Kg is equal to = $\frac{6236.91}{907.185} = 6.875 KWh/Kg$

To power 75 watts of bulb the amount of natural gas burned was = $\frac{246.375}{6.875}$ =

So, 35.836 Kg of natural gas was burned in one year to power the light bulb for 9 hours.

Amount of natural gas burned for one day = $\frac{35.836}{365} = 0.098 Kg$

Therefore, 0.098 Kg of natural gas burned for one day.

Now, we know that by international conventions the amount of CO₂ emitted to in burning 1 Kg of natural gas = 0.2 Kg of CO₂

Therefore CO₂ emitted in one day = 0.098$\times$0.2 = 0.0196 Kg = 19.6 grams of CO₂

Therefore, we found that 19.6 grams of Carbon dioxide gas is emitted to power 75 watt of bulb for 9 hours continuously.