Video Transcript
In an experiment, 80 grams of water
was measured and placed into a copper container, and its temperature was
recorded. A spirit lamp containing a fuel was
weighed and then placed underneath the copper container. The wick of the spirit lamp was
lit, and the water was heated until the temperature reached 50 degrees Celsius. The flame was then extinguished,
and the final temperature of the water was recorded. The spirit lamp was then also
weighed. The results are listed in the table
below. What is the value of 𝑞, the heat
energy transferred, in the experiment? Give your answer in units of
kilojoules and to one decimal place. Use a value of 4.18 joules per gram
per degree Celsius for the specific heat capacity of water.
The information on the screen takes
up quite a lot of space, so let’s represent it in a different way. The question tells us that 80 grams
of water was measured and placed into a copper container. Its temperature was recorded at
22.5 degrees Celsius. A spirit lamp containing fuel was
weighed and placed underneath the copper container. The spirit lamp had a mass of 54.38
grams. The wick of the spirit lamp was
lit, and the water was heated until the temperature reached 50 degrees Celsius. The flame was then extinguished,
and the final temperature of the water was recorded at 51.2 degrees Celsius. The spirit lamp was then also
weighed and had a mass of 52.88 grams. So, we have been given the
temperature of 80 grams of water and the mass of the spirit lamp before the wick of
the spirit lamp was lit and after it was lit.
We are being asked to calculate the
amount of heat energy transferred to 80 grams of water when a fuel is combusted. We can calculate the amount of heat
energy 𝑞 using the following equation: 𝑞 equals 𝑚 times 𝑐 times Δ𝑇. 𝑞 is the heat energy in joules, 𝑚
is the mass in grams, 𝑐 is the specific heat capacity in joules per gram per degree
Celsius, and Δ𝑇 is the temperature change in degree Celsius. From the question, we’re told that
the mass of water is 80 grams. We’ve also been given the specific
heat capacity of water, which is 4.18 joules per gram per degree Celsius. We haven’t explicitly been given
Δ𝑇, the temperature change, but we have been given the temperature of the water
before heating and after heating.
To find Δ𝑇, the temperature
change, we have to subtract the temperature of the water before heating from the
temperature of the water after heating. This gives a value of 28.7 degrees
Celsius. We now have the values for all
parts of the equation to calculate the heat energy. Before performing the calculation,
we can cancel some of the units. The gram units on the right side of
the equation will cancel and so will degree Celsius. If we perform this calculation, we
get a value of 9597.28 joules. So we’ve now calculated the heat
energy transferred to the water. But the value we have is in units
of joules, and the question asks for units of kilojoules.
Kilo- means 1000, so one kilojoule
is equivalent to 1000 joules. So to convert our answer in joules
to units of kilojoules, we can use the conversion one kilojoule per 1000 joules. The joule units cancel. And if we perform the calculation,
we get a value of 9.59728 kilojoules. So we now have the value of heat
energy transferred to water in units of kilojoules. But the question also asks for the
value to be given to one decimal place. 9.59728 kilojoules to one decimal
place is 9.6 kilojoules. So the answer to the question “What
is the value of 𝑞, the heat energy transferred, in the experiment?” is 9.6
kilojoules.
What is the heat change per gram of
fuel? Give your answer in units of
kilojoules per gram of fuel.
We have already calculated the
amount of heat energy that is transferred when the fuel is combusted. But we now need to calculate the
heat change per gram of fuel, so we need to consider the mass of the fuel in the
spirit lamp. To calculate the change in mass of
something, you need to subtract the final mass from the initial mass.
Since this question concerns the
mass of the fuel and the spirit lamp contains the fuel, we need to subtract the
final mass of the spirit lamp from the initial mass of the spirit lamp. The initial mass of the spirit lamp
is 54.38 grams, and the final mass of the spirit lamp is 52.88 grams. So we need to subtract 52.88 grams
from 54.38 grams. This gives a value of 1.5
grams. This tells us that burning 1.5
grams of fuel produces 9.6 kilojoules of heat. Therefore, the heat change is 9.6
kilojoules per 1.5 grams of fuel.
The question asks for the heat
change per gram of fuel. To go from 1.5 grams of fuel to one
gram of fuel, you have to divide by 1.5. So to find the heat change per gram
of fuel, we also need to divide 9.6 kilojoules by 1.5. This gives a value of 6.4
kilojoules. The question asks for the answer to
be given in units of kilojoules per gram of fuel. So the answer to the question “What
is the heat change per gram of fuel?” is 6.4 kilojoules per gram.
