A Big Mac hamburger from McDonald’s contains 540 Calories.
(a) How many kilojoules does a Big Mac contain?
(b) For how many hours could the amount of energy in a
Big Mac light a 100-watt light bulb? (1 watt = 1 J/s)
The answers I got were:
a) 2259.36 kJ
b) 6.276 hours
Am I correct?
I agree with both answers. I note that you used too many significant figures in the answers.
How would you right the answers so there are enough significant figures?
Here is a site that does a really good job of explaining both significant figures as well as how to inject that into multiplying/dividing and addition/subtraction.
https://www.chemteam.info/SigFigs/SigFigs.html
Assuming you know how to determine the number of s.f. in a problem, then for addition/subtraction the s.f. in the answer can be no more than the least accurate in the numbers. That is
1234.11
+1234.1
-----------------------
= 2468.2
Note that the first number is known to the hundredths place but the second number is known only to the tenths; therefore, the answer may not be more accurate than the tenths. There is another rule when multiplying/dividing but that is done very well in the link I gave you above.
To answer these questions, we can use the conversion factor between kilocalories (Calories) and kilojoules (kJ), as well as the power and time relationship for the light bulb. Let's break down each question:
(a) To convert calories to kilojoules, we need to multiply the number of calories by the conversion factor of 4.184 kJ/cal:
Calories * 4.184 kJ/cal = kilojoules
In this case, the Big Mac contains 540 Calories. Let's do the calculation:
540 Calories * 4.184 kJ/cal = 2253.36 kJ
Therefore, the correct answer is:
a) The Big Mac contains 2253.36 kilojoules.
(b) To determine how long the energy in a Big Mac could light a 100-watt light bulb, we need to divide the total energy in kilojoules by the power of the light bulb in watts:
kilojoules / watts = seconds
However, the question asks for the duration in hours. To convert seconds to hours, we divide by 3600 seconds/hour:
seconds / 3600 = hours
Using the energy of the Big Mac from part (a), let's calculate the duration:
2253.36 kJ / 100 W = 22.5336 seconds
22.5336 seconds / 3600 s/h = 0.00626 hours
Therefore, the correct answer is:
b) The amount of energy in a Big Mac can light a 100-watt light bulb for approximately 0.00626 hours, which rounds to 0.00626 or approximately 0.0063 hours.
So, your answers are almost correct:
a) It should be 2253.36 kJ (you had a typo in your answer).
b) It should be approximately 0.0063 hours.