1. An electric space heater draws 15.0 A from a 120 V source. It is operated, on average, for 5.0h (hours) each day. a) How much power does the heater use and b) At $.10 per kWh, what does it cost to operate the heater for 30 days?

2. Suppose each person in the United States uses 12,000 kWh of electricity a year and the power plants using coal to generate electricity are 40% efficient. If 1.0 kg of burned coal releases 33.0 mJ a) how much coal will be burned during a year for a family of four b) how large a pile of coal would that be (using 2620 kg/ m^3) c) how much heat is given off to the environment
3. A light bulb uses 65 watts (used for 6 hours a day) and a digital clock uses 5 watts (used for 24hrs a day). Find the cost of operating each one for 30 days. Assume the price is $.10 per kWh

The equations given=
power= current x voltage, energy= power x time, cost= energy x price

I can find a) at 1800 w (watts), but I have no idea where to start on part b.
For 2, I'm unsure of where to star. I know the family of four would use 48,000 kWh a year, but after that, I'm lost. Could you please help explain it to me?

1a) The heater uses 1800 W (watts) of power.

1b) The cost to operate the heater for 30 days is 1800 W x 5.0 h x 30 days x $.10/kWh = $540.

2a) The amount of coal burned during a year for a family of four is 48,000 kWh x 1.0 kg/33.0 mJ x 40% efficiency = 57600 kg.

2b) The pile of coal would be 57600 kg/2620 kg/m^3 = 22 m^3.

2c) The amount of heat given off to the environment is 48,000 kWh x 1.0 kg/33.0 mJ = 14400 MJ.

3a) The cost of operating the light bulb for 30 days is 65 W x 6 h x 30 days x $.10/kWh = $117.

3b) The cost of operating the digital clock for 30 days is 5 W x 24 h x 30 days x $.10/kWh = $72.

Sure! Let's start with question 1.

a) To find the power used by the electric space heater, we can use the equation:
Power = Current x Voltage

Given that the heater draws 15.0 A from a 120 V source, we can plug these values into the equation:
Power = 15.0 A x 120 V = 1800 W

So, the electric space heater uses 1800 watts of power.

b) To find the cost of operating the heater for 30 days, we need to calculate the energy used first. The equation for energy is:
Energy = Power x Time

Given that the heater is operated for 5.0 hours each day and we want to calculate the cost for 30 days, we can plug these values into the equation:
Energy = 1800 W x 5.0 h/day x 30 days = 270,000 Wh (watt-hours)

To convert watt-hours to kilowatt-hours, we divide by 1000:
Energy = 270,000 Wh / 1000 = 270 kWh

Now, we can calculate the cost using the equation:
Cost = Energy x Price

Given that the price is $0.10 per kWh, we can plug in the values:
Cost = 270 kWh x $0.10/kWh = $27.00

Therefore, the cost to operate the electric space heater for 30 days would be $27.00.

Moving on to question 2.

a) To calculate the total energy used by a family of four in a year, we multiply the energy used by each person (12,000 kWh) by the number of people (4):
Total Energy = 12,000 kWh/person x 4 people = 48,000 kWh

b) To find the mass of coal burned during a year, we need to know the efficiency of coal power plants. Given that they are 40% efficient, we can use the formula:
Efficiency = Energy Output / Energy Input

Since energy input is equal to the energy used by the family of four (48,000 kWh), we can rearrange the equation to solve for energy output:
Energy Output = Efficiency x Energy Input
Energy Output = 0.40 x 48,000 kWh = 19,200 kWh

To convert this energy to joules, we use the conversion factor 1 kWh = 3.6 x 10^6 J:
Energy Output = 19,200 kWh x 3.6 x 10^6 J/kWh = 6.912 x 10^10 J

Now, to find the mass of coal burned, we divide the energy released by burning 1 kg of coal (33.0 mJ) by the energy output:
Mass of Coal = Energy Output / Energy Released per kg of Coal
Mass of Coal = (6.912 x 10^10 J) / (33.0 x 10^-3 J/kg) = 2.094 x 10^12 kg

c) To calculate the volume of the coal pile, we need to know the density of coal (2620 kg/m^3). We can use the formula:
Volume = Mass / Density
Volume = (2.094 x 10^12 kg) / (2620 kg/m^3) = 7.986 x 10^8 m^3

Finally, we move on to question 3.

To find the cost of operating the light bulb and digital clock for 30 days, we can use the equations given.

For the light bulb:
Power = 65 W (Given)
Time = 6 hours/day
Energy = Power x Time = 65 W x 6 h = 390 Wh

To convert watt-hours to kilowatt-hours, we divide by 1000:
Energy = 390 Wh / 1000 = 0.39 kWh

Cost = Energy x Price = 0.39 kWh x $0.10/kWh = $0.039

So, the cost of operating the light bulb for 30 days would be $0.039.

For the digital clock:
Power = 5 W (Given)
Time = 24 hours/day
Energy = Power x Time = 5 W x 24 h = 120 Wh

To convert watt-hours to kilowatt-hours, we divide by 1000:
Energy = 120 Wh / 1000 = 0.12 kWh

Cost = Energy x Price = 0.12 kWh x $0.10/kWh = $0.012

Therefore, the cost of operating the digital clock for 30 days would be $0.012.

I hope this explanation helps you understand how to approach and solve these problems!

Sure! Let's break down each question step-by-step.

1a) To find the power used by the heater, we can use the formula Power = Current x Voltage. Given that the heater draws 15.0 A from a 120 V source, we can calculate the power as follows:

Power = 15.0 A x 120 V
Power = 1800 W

So, the heater uses 1800 Watts of power.

1b) To calculate the cost of operating the heater for 30 days, we need to find the energy consumed and then multiply it by the price per kilowatt-hour (kWh).

First, let's calculate the energy consumed by the heater. Since it is operated on average for 5.0 hours each day, we can use the formula Energy = Power x Time:

Energy = 1800 W x 5.0 h/day
Energy = 9000 Wh (Watt-hours)

Now, let's convert the energy into kilowatt-hours (kWh) by dividing it by 1000:

Energy = 9000 Wh ÷ 1000
Energy = 9 kWh

Next, we can calculate the cost by multiplying the energy consumed by the price per kWh:

Cost = 9 kWh x $0.10/kWh
Cost = $0.90

So, it would cost $0.90 to operate the heater for 30 days at a rate of $0.10 per kWh.

2a) To calculate the amount of coal burned during a year for a family of four, we need to multiply the electricity usage per person by the number of people in the family. Given that each person uses 12,000 kWh of electricity per year and there are four people in the family, the total electricity usage for the family is:

Total Electricity Usage = 12,000 kWh/person x 4 people
Total Electricity Usage = 48,000 kWh

2b) To determine the size of the coal pile, we can use the energy released per kilogram of burned coal and the density of coal. Since 1.0 kg of burned coal releases 33.0 mJ and the density of coal is 2620 kg/m^3, we can calculate the volume of coal:

Volume of Coal = Total Energy / Energy per kilogram
Volume of Coal = (48,000,000 Wh x 3.6 x 10^6 J/Wh) / (33.0 x 10^-3 J/kg)
Volume of Coal = (48,000,000 x 3.6) / 0.033
Volume of Coal = 5,280,000,000 cubic meters

2c) Finally, to calculate the amount of heat given off to the environment, we need to consider the efficiency of power plants. Since coal power plants are 40% efficient, the total energy generated by burning coal is:

Total Energy Generated = Total Electricity Usage / Efficiency
Total Energy Generated = 48,000 kWh / 0.40
Total Energy Generated = 120,000 kWh

So, the total heat given off to the environment is 120,000 kWh.

3) To calculate the cost of operating the light bulb and the digital clock for 30 days, we can use the formula Cost = Energy x Price. Given that the light bulb uses 65 watts (for 6 hours a day) and the digital clock uses 5 watts (for 24 hours a day), let's calculate the energy consumed by each device:

Energy of Light Bulb = 65 W x 6 h/day
Energy of Light Bulb = 390 Wh (Watt-hours)

Energy of Digital Clock = 5 W x 24 h/day
Energy of Digital Clock = 120 Wh (Watt-hours)

Now let's calculate the cost for each device:

Cost of Light Bulb = 390 Wh ÷ 1000 x $0.10/kWh
Cost of Light Bulb = $0.039 (or $0.04 rounded to two decimal places)

Cost of Digital Clock = 120 Wh ÷ 1000 x $0.10/kWh
Cost of Digital Clock = $0.012 (or $0.01 rounded to two decimal places)

So, operating the light bulb for 30 days would cost approximately $0.04, and operating the digital clock for 30 days would cost approximately $0.01.