Electric Power Problems
- It's a cool day, about 10 oC, so you plan to make about
5.0 kg of clear soup using your slow cooking crockpot. To
decide whether the soup will be ready for dinner, you
estimate how long it will take before the soup gets to
its boiling point. Before adding the ingredients, you
turn the crockpot over and read that it is a 200-ohm
device that operates at 120 volts. Since your soup is
mostly water, you assume it has the same thermal
properties as water, so its specific heat capacity is
4200 J/(kg oC) and its heat of vaporization is 2.3 x 106
J/kg.
- You are working with a company that has the contract to
design a new, 700-foot high, 50-story office building in
Minneapolis. Your boss suddenly bursts into your office.
She has been talking with an engineer who told her that
when the elevator is operating at maximum speed, it would
take the 6500-lb loaded elevator one minute to rise 20
stories. She thinks this is too long a time for these
busy executives to spend in an elevator after returning
from lunch at the Minneapolis Athletic Club. She wants
you to buy a bigger power supply for the elevator. You
look up the specifications for the new supply and find
that it is the same as the old one except that it
operates at twice the voltage. Your boss's assistant
argues that the operating expenses of the new power
supply will be much more than the old one. Your boss
wants you to determine if this is correct. You estimate
that while the elevator runs at maximum speed, the whole
system, including the power supply, is 60% efficient. The
cost of electricity is $0.06 per kilowatt-hour
(commercial rate).
- You have finally graduated from college and found a job
with the Washington State Agricultural Concerns Group.
Farmers and fishermen are concerned that the rate that
water flows in the Columbia river, which is controlled by
dams, will not be adequate for both irrigation needs and
salmon spawning. The dams control the river's flow rate
to produce most of the electrical power for cities along
the West Coast. Your group leader assigns you the task of
calculating the volume of water per second (flow rate)
which normally would flow through the Grand Coulee Dam,
the largest on the Columbia River. She tells you that
this dam typically generates 2000 megawatts (MW) of power
and is 50% efficient in converting the water's energy to
electrical energy. The dam is 170 meters high ,and the
water is kept in a lake 10 meters below the top of the
dam. The Columbia River is 170 meters wide at the dam.
The density of water is 1.00 g/cm3.