Video Transcript
A student wants to take 150
milliliters of water at 25 degrees Celsius and boil it. They are given some fuel that
produces 6.75 kilojoules of heat energy per one gram of fuel burned. How much fuel does the student need
to burn in order for the water to reach its boiling point? Give your answer to the nearest
whole number. Assume the heat capacity of water
remains constant.
There’s a lot of information in
this question, so let’s break it down. A student has 150 milliliters of
water at 25 degrees Celsius. They want to boil the water. Water boils at 100 degrees
Celsius. So the student will need to
increase the temperature of the water by 75 degrees. To do this, the student is given a
fuel to burn. We are told that 6.75 kilojoules of
heat energy is produced per one gram of fuel burned. We need to assume for this question
that all of the heat energy produced by the fuel is transferred to the water when in
reality some of this energy would be transferred to the surroundings. Using all of this information, we
need to determine how much fuel needs to be burned in order for the water to
boil.
To answer the question, we’ll first
need to determine the amount of energy needed to boil the water. For this, we’ll need to use the
equation 𝑞 equals 𝑚𝑐Δ𝑡. In this equation, 𝑞 is the energy
in joules, 𝑚 is the mass in grams, 𝑐 is the specific heat capacity in joules per
gram per degree Celsius. The specific heat capacity, as the
unit suggests, is the amount of energy in joules required to raise the temperature
of one gram of a substance by one degree Celsius. Finally, Δ𝑡 represents the change
in temperature in degrees Celsius.
To determine 𝑞, the amount of
energy needed to boil the water, we need to identify 𝑚, 𝑐, and Δ𝑡. We were given the volume of water,
not the mass. But we can make use of the fact
that one milliliter of water has a mass of one gram. So 150 milliliters of water has a
mass of 150 grams.
Next, we need to recall that the
specific heat capacity of water is 4.184 joules per gram per degrees Celsius. This value does change slightly as
the temperature of water increases. But we are told in the question to
assume it is constant.
Finally, we know that the
temperature of the water needs to increase from 25 degrees Celsius to 100 degrees
Celsius. This means that the change in
temperature is 75 degrees Celsius. We can then plug the values for 𝑚,
𝑐, and Δ𝑡 into the equation. The gram and degrees Celsius units
will cancel, leaving us with the unit joules. Performing the calculation gives us
an answer of 47070 joules.
We could also report this value in
kilojoules by recognizing that 1000 joules is equal to one kilojoule. We can convert from joules to
kilojoules by multiplying by one kilojoule per 1000 joules. The joule units will cancel, and
we’ll get a value of 47.07 kilojoules.
Now that we know the amount of
energy needed to boil the water, we can determine the mass of fuel needed to supply
this amount of energy. We know that each gram of fuel
burned will release 6.75 kilojoules of heat energy. So, to calculate the mass, we can
divide the amount of energy required by the amount of energy released per gram of
fuel. The kilojoule units will cancel,
leaving us with the unit grams. Performing the calculation gives us
an answer of 6.973 grams.
The question asks us to give our
answer to the nearest whole number. So, to the nearest whole number,
the amount of fuel the student needs to burn in order for the water to reach its
boiling point is seven grams.
