Coal burned per hour to power 260 million electric clocks

[phystudent]

I need help on what formulas to use and how to start this physics problem.

We estimate that there are 260 million plug-in electric clocks in the United States, approximately one clock for each person. The clocks convert energy at the average rate of 3.6W.
To supply this energy, how many metric tons of coal are burned per hour in coal fired electrci-generating plants that are, on average, 13.4% efficient? The heat of combustion for coal is 33MJ/kg. Answer in units of metric tons.

Another question, how is Watts a rate?

 

[jamesrc]

Watts is a rate because it is a measure of power and power is the rate of doing work (or using energy). 1 Watt = 1 Joule/second

For this problem:

The total power consumed is (260,000,000)3.6W = 936 MW

So:

(13.4%)*(33MJ/kg)*(mass of coal)/(1hour) = 936 MW

The amount of useful energy is given by the efficiency multiplied by the energy content of the coal multiplied by the amount of coal.

Take care of your units properly and solve for the mass of coal burned in an hour.

 

[M98Ranger]

To solve this problem, we will use the formula P = E/t, where P is power in watts, E is energy in joules, and t is time in seconds. We can also use the formula P = IV, where I is current in amperes and V is voltage in volts.

First, we need to calculate the total energy used by all the electric clocks in the United States per hour. To do this, we multiply the power of one clock (3.6W) by the total number of clocks (260 million). This gives us a total power of 936 million watts or 936 MW.

Next, we convert this power to energy by multiplying it by the time in hours (1 hour). This gives us a total energy of 936 million watt-hours or 936 MWh.

Now, we can use the formula E = P*t to calculate the amount of coal needed to supply this energy. We know that the efficiency of coal-fired electric-generating plants is 13.4%, which means that only 13.4% of the energy produced by burning coal is converted into electricity. Therefore, we divide the total energy (936 MWh) by the efficiency (13.4%) to get the total energy produced by burning coal, which is 6,985 MWh.

To convert this energy to metric tons of coal, we need to use the heat of combustion for coal (33 MJ/kg). We can convert the energy from MWh to MJ by multiplying by 3.6 (1 MWh = 3.6 MJ). Then, we divide the total energy (25,146 MJ) by the heat of combustion (33 MJ/kg) to get the total amount of coal needed, which is approximately 762 metric tons.

Therefore, to supply the energy needed for all the electric clocks in the United States per hour, approximately 762 metric tons of coal must be burned in coal-fired electric-generating plants.

As for your second question, watts is a unit of power, which is the rate at which energy is transferred or converted. In this case, the power of 3.6W represents the rate at which energy is being converted by each electric clock. This is why we use the formula P = E/t, where E is energy and t is time, to calculate the total energy used by the clocks. I hope this helps!