How Does Increasing Compression Ratio Affect CO2 Emission in Otto Cycle Engines?

[alex_b93]

Homework Statement

Estimate the change in volume of carbon dioxide if 'r' is increased from 10 to 11 (10% increase).

Assume 30 million cars, all use 1m^3 of fuel each year

Homework Equations

Efficiency of an Otto Cycle
η=1-r^(1-gamma)

The Attempt at a Solution

Original η=1-10^(1-gamma)
Final η=1-11^(1-gamma)

I then looked up a typical value of gamma (1.3), and worked out the efficiency of each

Original = 0.4988
Final = 0.5129

Not sure if this is right, as you weren't given the value of gamma.

Then I'm not entirely sure how to work out how much CO2 is produced from each m^3 of fuel, is it just multiplying by the efficiency?
Or have I gone completely wrong?

 

[anathema]

I appreciate your attempt at solving this problem. However, I believe there may be a misunderstanding of the question. The question is asking for an estimate of the change in volume of carbon dioxide, not the change in efficiency.

To estimate the change in volume of carbon dioxide, we can use the ideal gas law, PV = nRT. In this case, we can assume that the number of moles of carbon dioxide produced is directly proportional to the amount of fuel used. Therefore, if we increase the amount of fuel used by 10%, we can estimate that the amount of carbon dioxide produced will also increase by 10%.

Using this assumption, we can estimate the change in volume of carbon dioxide as follows:

Initial volume of carbon dioxide = 30 million cars x 1 m^3 of fuel x n moles of carbon dioxide
Final volume of carbon dioxide = 30 million cars x 1.1 m^3 of fuel x n moles of carbon dioxide

The change in volume of carbon dioxide can be calculated as:

Change in volume = Final volume - Initial volume
= (30 million cars x 1.1 m^3 of fuel x n moles of carbon dioxide) - (30 million cars x 1 m^3 of fuel x n moles of carbon dioxide)
= 30 million cars x 0.1 m^3 of fuel x n moles of carbon dioxide

Therefore, the estimated change in volume of carbon dioxide is 30 million cars x 0.1 m^3 of fuel x n moles of carbon dioxide.

I hope this helps clarify the question and provides a solution to your problem. Keep up the good work in your scientific endeavors!