a mordern power station,or, more correctly, an energy station, converts heat energy into electrical energy at an efficiency od 50% if the station produces electrical energy at a rate of 1.00GW from burning coal, calculate the mass of coal it burns each day. the coal it uses produces 25.0MJ of heat per kg when it burns completely.
i knows that 1.00W =1.00Js-
and i forgot about the formula...can someone help?
Energy= efficiency*power*time
Remember that a watt is a joule/second, so time has to be in seconds (seconds in a day...)
To calculate the mass of coal burned per day by the power station, we can use the formula:
Energy = Efficiency * Power * Time
First, let's convert the electrical power from gigawatts (GW) to watts (W):
1 GW = 1 * 10^9 W
Now we can substitute the given values into the formula:
Energy = 0.50 * (1 * 10^9 W) * Time
To find the time in seconds, we need to convert it from a day to seconds:
1 day = 24 hours * 60 minutes * 60 seconds = 86,400 seconds
So, the final formula becomes:
Energy = 0.50 * (1 * 10^9 W) * 86,400 seconds
Now, let's look at the heat energy produced by the burning of coal. The energy produced per kilogram of coal is given as 25.0 MJ (megajoules). To convert this to joules, we need to multiply it by 1,000,000 (since 1 MJ = 1,000,000 J).
Energy per kilogram of coal = 25.0 MJ * 1,000,000 J/MJ = 25,000,000,000 J/kg
Next, we can set up an equation equating the electrical energy produced in the power station to the heat energy released by burning coal:
Energy = Mass of coal burned * Energy per kilogram of coal
Substituting the values, the equation becomes:
0.50 * (1 * 10^9 W) * 86,400 s = Mass of coal burned * 25,000,000,000 J/kg
Now we can solve for the mass of coal burned per day:
Mass of coal burned = (0.50 * (1 * 10^9 W) * 86,400 s) / 25,000,000,000 J/kg
Evaluating the expression in the numerator:
0.50 * (1 * 10^9 W) * 86,400 s = 43,200,000,000 J
Final calculation:
Mass of coal burned = (43,200,000,000 J) / 25,000,000,000 J/kg
This simplifies to:
Mass of coal burned = 1.728 kg
Therefore, the power station burns approximately 1.728 kilograms of coal each day.