Dimensional analysis.

[can't_think_of_a_name]

Lily's car has a fuel efficiency of 88 liters per 100100100 kilometers.

What is the fuel efficiency of Lily's car in kilometers per liter?

 

My initial reaction is to go   (8 L/ 100 km)  (?km/?L). The question marks just represent some variables in algebra. I just seem to drawing a blank what the numbers are. It is probably pretty obvious.
 

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:working-units/x2f8bb11595b61c86:rate-conversion/v/dimensional-analysis-units-algebraically

 

I am using the link above to learn about dimensional analysis.

[studiot]

6 hours ago, can't_think_of_a_name said:

Lily's car has a fuel efficiency of 88 liters per 100100100 kilometers.

Really  ?

[joigus]

11 hours ago, can't_think_of_a_name said:

Lily's car has a fuel efficiency of 88 liters per 100100100 kilometers.

Really?

Lily's car is THE solution to global warming.

Edited September 12, 2020 by joigus

[timo]

9 minutes ago, joigus said:

Lily's car is THE solution to global warming.

It isn't. Car traffic makes up ~10% of the world's energy-related emissions (https://www.fia.com/sites/default/files/global_reduction_in_co2_emissions_from_cars-_a_consumers_perspective_0.pdf [*]), and that's not even considering construction, agriculture, forest fires, melting of permafrost ground, methane-release from the sea, etc.

 

Assuming the thread is not about how realistic the consumption values are: I did not follow the link, but there are two (related) ways to solve such questions:

1) First try to find out how much the consumption would be per single km. Then, from that number find out the consumption per 100 km (hint: it's 100 times the number before).

2) If you know how to solve equations, solve "88 l / 100100100 km = x / 100 km" for x. I strongly advise to try solving it in the form I wrote down, i.e. including the units, not as "88/100100100 = x/100". Especially since the thread title is "Dimensional Analysis".

 

 [*]: I am totally aware that this is a car lobby publication and that their choice of world-wide values has probably been to downplay the share in the major car markets. But I have no reason to doubt the approximate value.

[joigus]

57 minutes ago, timo said:

It isn't. Car traffic makes up ~10% of the world's energy-related emissions (https://www.fia.com/sites/default/files/global_reduction_in_co2_emissions_from_cars-_a_consumers_perspective_0.pdf [*]), and that's not even considering construction, agriculture, forest fires, melting of permafrost ground, methane-release from the sea, etc.

Assuming the thread is not about how realistic the consumption values are:[...]

Yes, you're right. Thank you. I was just drawing attention to (very likely) misread data. I was joking. I should have used  instead of . Or maybe  or 🤣.

The point, if any, I was trying to make is that, if Lilly's car can go one hundred million + kilometers with 88 lt., and the same efficiency could be applied to every engineering process that produces CO₂, we wouldn't be in as much of a problem as we are with carbon emissions. But never mind.

[HallsofIvy]

"Lily's car has a fuel efficiency of 88 liters per 100100100 kilometers.

What is the fuel efficiency of Lily's car in kilometers per liter?"

I am going to assume that is 88 liters per 100 kilometers.  

88 kilometers per liter=  88 liters/100 kilometers= 0.88 liters/km

Now take the reciprocal: (1/0.88)(km/liter}= 1.136... km/liter.

Edited September 25, 2020 by HallsofIvy

[OldChemE]

On 9/11/2020 at 7:47 PM, can't_think_of_a_name said:

Lily's car has a fuel efficiency of 88 liters per 100100100 kilometers.

What is the fuel efficiency of Lily's car in kilometers per liter?

 

My initial reaction is to go   (8 L/ 100 km)  (?km/?L). The question marks just represent some variables in algebra. I just seem to drawing a blank what the numbers are. It is probably pretty obvious.
 

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:working-units/x2f8bb11595b61c86:rate-conversion/v/dimensional-analysis-units-algebraically

 

I am using the link above to learn about dimensional analysis.

By now I presume you will have already found your answer.  But-- if you are still struggling with dimensional analysis maybe a teacher's perspective will help.

1.. You have two pieces of information:  liters used and km traveled, but the question asks for efficiency in km/L

So, step 1: you need numbers arranged in a ratio that matches the desired answer.  It wants km/L (a ratio), so the ratio has to match:  100100100 km/88 L  Here, we made a ratio using the actual numbers making it so that the km's are on top and the L's on the bottom so that it matches the units in the required answer.

Step 2, do the math (100100100 divided by 88)

Step 3:  you now have a number that has the units of km/L  this is your answer.

Think about this:  We look at the dimensions that the answer is supposed to have, and form our ratio so that the arrangement of the dimensions we have matches the arrangement of the required answer (that is, km on top of the fraction and liters on the bottom).  Then, we put in the numbers in the same arrangement and do the math.  This is what Dimensional Analysis is all about:  Using the dimensions of the answer we want to decide where to put the numbers in the math.