Given that 1 kcal of
heat is required to increase the temperature of 1 kg of water by
1°C:
How many kcals would
be required to heat 100 kg of water by 20°C for a bath?
How many joules is
this?
How many Btus?
If your water heater
can supply 40 kBtu/h, how long will it take to heat this water?
a. Given that 1 kWh =
3.6 MJ and that 1 Btu = 1055 J, show that 1 kWh = 3412 Btu.
Why would it be
incorrect to use this conversion factor directly to determine the
amount of coal required to generate electricity in a power plant?
A typical home in the
northern U.S. might require 120 MBtu of heat for the average winter.
If this heat were
supplied by a natural gas furnace operating at 60 percent
efficiency,
How many BTU is
needed?
How many cubic feet
of gas would need to be purchased?
At a cost of
$0.90/ccf, what would it cost to heat this house for one season?
If a new 80 percent
efficient furnace could be installed at a cost of $4,000
How many Btu for
the new furnace?
How many ccf?
What would it cost
to heat this house for one season with the
new furnace?
How long would it
take to pay back the cost of this furnace assuming gas prices
remained the same?
Suppose the house in
question 3 is located in Cleveland where the annual average solar
flux is 160 W/m^{2}2.
If 10 m^{2} of solar
panels operating at 20 percent efficiency were installed on this
house to collect and store solar energy in the form of hot water:
How much energy
could be gained in one year in this manner?
What fraction of the
annual heating requirement is this?
Using the hotwater
heating requirements for a bath from question 1(c), how many hot
baths would this energy supply in one year?
The annual average
solar flux in Tucson is 250 W/m^{2}.
Suppose 10 m^{2} of
solar electric panels operating at 10 percent efficiency were
installed on a home there.
How many kilowatts
would be collected?
How many kWh of
electricity would these panels collect in one year?
What fraction of the
annual electrical requirement of 10,000 kWh for the average home
does this represent?
How many square
meters of solar panels would be required to supply 10,000 kWh per
year?
Solar energy is
converted naturally into wood biomass with an efficiency of about
0.1 percent. Suppose a wood lot of 100 hectares (10^{6}
m^{2}) is located in
Missouri, where the average annual solar flux is 200 watts/m^{2}.
Given that the heat value for wood is 12 MBtu/ton,
The wood is
equivalent to how many kilowatts?
How many
kilowatthours for the year?
How many BTU’s?
How many tons of
wood can be produced by this property each year?
With moderate winds,
a modern large wind turbine can generate about 250 kW of
electricity, whereas a large nuclear power plant can generate 1,000
MW.
How many wind
turbines would be required to give the same output as one nuclear
power plant?
Discuss some of the
advantages and disadvantages to providing electrical power by each
method.
Batteries are usually
rated in terms of amperehours, indicating the current that the cell
is capable of delivering for a specified time. Typical Dcell
flashlight batteries might be rated at 3 amperehours. The total
electrical energy available from such a battery is found by
multiplying the amperehour rating by the battery voltage. Thus this
same 1.5 volt D cell could deliver 4.5 watthours of electrical
energy.
Convert this energy
to kWh and compare the cost of electrical energy derived in this
manner to that of standard "gridbased" electricity.
Assume that the battery costs $1.00 and that electricity from the
power company is available at $0.10/kWh.
The table below gives
prices and heat energy content for various fuels that are commonly
used for home heating. Fuel prices are given as a perunit cost for
fuel delivered to the home. Complete the table by filling in the
last two columns and then compare the cost of home heating by these
various methods. In your computations, assume that the home requires
120 MBtu of heat for a season and that gas or oilfired furnaces
operate at 80 percent efficiency. Assume that electrical heating is
100 percent efficient.
Fuel

Price

Energy Content of Fuel

Cost per MBtu

Cost of Home Heating

Nat. gas

$1.14/ccf

1030 Btu/cf



Propane

$1.69/gal

92 k Btu/gal



Fuel oil

$1.93/gal

133 k Btu/gal



Electricity

$0.10/kWh

3412 Btu/kWh



The complete
combustion of gasoline produces water and CO_{2}
as products.
2C_{8}H_{18}
+ 25O_{2}
16CO_{2} + 18H_{2}O
For each gasoline
molecule, how many CO_{2 }molecules
are produced?
What is the
molecular mass for the gas (C_{8}H_{18})
and for CO_{2}?
For each gallon of
gasoline (6 pounds) used, how pounds of CO_{2}
are produced?
If you have a car
the gets 25 miles per gallon, how pounds of CO_{2}
do you produce per mile?
The car goes 12,000
miles per year, how pounds of CO_{2}
are produced per year?
How many tons of CO_{2}
do you produce per year?
If there are 250
million cars in use in the United States, how many tons of CO_{2}
are produced per year?
