Compression ratio and volume reduction of CO2

[StillAnotherDave]

Homework Statement

If the compression ratio of car engines is increased by 10% (from 10 to 11), estimate the volume reduction in annual CO2 emission. Assume there are 30 million cars each consuming one cubic meter of fuel annually.

Relevant Equations

$η=1-r^(1-γ)$ where $γ=1.4$
$r=V_1/V_2$

The question is: If the compression ratio of car engines is increased by 10% (from 10 to 11), estimate the volume reduction in annual CO2 emission. Assume there are 30 million cars each consuming one cubic meter of fuel annually.

The question is looking for a rough estimate for an answer.

I have some basic ideas but can't quite put them together:

1. Assuming one cubic meter of fuel, that would be around 900kg of carbon giving 75000 moles. At a volume of approximately 20 litres (0.02 cubic meters) per mole, this would be 1500 cubic meters of $CO_2$ per vehicle.

2. I think the question would also involve working out the percentage difference in $CO_2$ volume by approximating the difference in environmental pressure and temperature..

I'd appreciate any help. Not quite sure how to work through this.

 

[StillAnotherDave]

Initial thought:

Is this a simple case of comparing efficiencies to find how much fuel each car consumes given the change in $r$?

$$η_1 = 1 - 10^-0.4 = 0.60189$$

For $r=11$:

$$η_2 = 1 - 11^-0.4 = 0.61678$$

This means each car consumes a factor of approx. 0.975 cubic meters of fuel given the higher compression ratio. Giving 1460 cubic meters of $CO_2$ annually compared 1500 originally. This seems too basic to be correct??

 

[StillAnotherDave]

Any help?

 

[StillAnotherDave]

Would still appreciate any pointers on how to get started...

 

[StillAnotherDave]

Wow.. looks like this one's got everyone stumped!

 

[berkeman]

One issue with the question is they say the cars consume the same amount of fuel annually no matter the engine efficiency. Would that not mean that the same amount of CO2 is given off?

 

[hutchphd]

One issue with the question is they say the cars consume the same amount of fuel annually no matter the engine efficiency

Gee I read the description that each car uses a cubic meter before the compression increase, and so slightly less after.
So (to the OP) figure how much less carbon is emitted per car and miltiply by 30 million.

 

[StillAnotherDave]

One issue with the question is they say the cars consume the same amount of fuel annually no matter the engine efficiency. Would that not mean that the same amount of CO2 is given off?

Hmm. My thought was (given the wording of the question) that the emission volume would be compression ratio dependent in some fashion. So, while the same volume of fuel is consumed, this would nonetheless reduce the emission quantity.

 

[hutchphd]

You are overthinking this. Efficiency =mileage.

 

[StillAnotherDave]

You are overthinking this. Efficiency =mileage.

How does the efficiency of the vehicle relate to how much CO2 it produces? And therefore, how does the change in η relate to the change in volume of CO2 emission?

 

[hutchphd]

It uses less fuel to perform the same daily functions.
Any other interpretation of the problem statement is foolishness.

 

[Merlin3189]

The volume emission at STP (or any other specified TP) will be proportional to the fuel used, assuming complete combustion.

 

[StillAnotherDave]

Thank you gentlemen. This was along the lines of my original solution but seemed far too simple an answer. Perhaps Covid has simply made question setters more compassionate.