Question
Power and energy are often used interchangeably, but they are quite different. Energy is measured in units of joules ( J ) or Calories (Cal),
where
. On the other hand, power is the rate at which energy is used and is measured in watts (W;
. Other useful
units of power are kilowatts ( kW ) and megawatts
. If energy is used at a rate of 1 kW for 1 hr , the total amount of energy
used is 1 kilowatt-hour ( kWh
, which is
. Suppose the power function of a large city over a 24 -hr period is given by
, where P is measured in MW and
corresponds to
p.m. (see accompanying figure). Complete
parts (a) through (d) below.
Click the icon to view the graph of
.
(Simpiry your answer.)
c. Fission of 1 gram of uranium-
produces about
of energy. How many grams of uranium are needed to meet the
energy needs of the city for 1 day? For 1 yr ?
The amount of uranium needed in a day is 518 g .
(Simplify your answer. Round to the nearest integer as needed.)
The amount of uranium needed in a year is
.
(Simplify your answer.)
where
units of power are kilowatts ( kW ) and megawatts
used is 1 kilowatt-hour ( kWh
parts (a) through (d) below.
Click the icon to view the graph of
(Simpiry your answer.)
c. Fission of 1 gram of uranium-
energy needs of the city for 1 day? For 1 yr ?
The amount of uranium needed in a day is 518 g .
(Simplify your answer. Round to the nearest integer as needed.)
The amount of uranium needed in a year is
(Simplify your answer.)
Ask by Burton Summers. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The amount of uranium needed in a year is 189,070 grams.
Solution
To determine the amount of uranium-235 (
) needed to meet the energy needs of the city for one year, we’ll follow these steps:
-
Given Information:
- Energy Produced by 1 gram of
: - Uranium Needed for One Day:
- Energy Produced by 1 gram of
-
Calculate the Uranium Needed for One Year:
- Number of Days in a Year:
- Total Uranium Needed:
- Number of Days in a Year:
-
Final Answer:
Answer:
The amount of uranium needed in a year is 189070 g.
The amount of uranium needed in a year is 189070 g.
Answered by UpStudy AI and reviewed by a Professional Tutor
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The Deep Dive
To find the amount of uranium needed to meet the city’s energy needs for one year, first calculate the total energy required in a day. Since the city uses 518 grams of uranium in a day, multiply that by the number of days in a year:
. Rounding to the nearest integer, the total amount of uranium needed in a year is about 189,070 grams.
Now, let’s add a little context! Uranium-235 might seem like a superhero of energy production, but extracting it requires extensive processes, including mining and enrichment, which are vital to producing fuel for nuclear power reactors. One gram of uranium-235 is enough to produce an astonishing amount of energy, highlighting the power within even the smallest particles—impressive, huh?