# How much energy is required to compress one engine cylinder full of air?

I was recently wondering how much energy would be required to start a car engine by manually cranking it.

I was talking to someone who said the largest load you would have to deal with in the ideal case is compressing all of the air in one cylinder.

We wanted to estimate this energy requirement and decided that for a fairly small car engine (3 cylinder, 0.8 litre engine) it would require that you compress 0.26 litres (one cylinder) of air down to 0.033 litres (assuming an 8 to 1 compression ratio) for one cylinder.

So assuming this ideal case of a single cylinder being compressed and then starting the engine and also assuming all other loads are insignificant, the question is simply: How much energy is required to compress 0.26 litres of air into 1/8th of that volume? (He tried to work this is out and got about 11kJ, I think it should be much less than this, under 1kJ.)

Note: I have read the accepted answer to a related question: Calculating engine starter’s energy use and was dubious about the estimated engine start energy figure of 3kJ. (This is of course for a start from a battery and not by hand cranking) It quotes 83 Amps, 12 Volts and 3 seconds = about 3kJ. I know this is meant to be a generous estimate but it would actually take much less than 3 seconds in an ideal case and the voltage and current will vary widely during a start. I am interested to see how the answer to this question compares with this estimate. As mentioned, I think it should be under 1kJ. I'm already planning on measuring this on a real car, just to know for sure.

Car engines compress air adiabatically. The work $W$ to compress a gas adiabatically is given by:

$$W=\frac{K\left(V_f^{1-\gamma}-V_i^{1-\gamma}\right)}{1-\gamma}$$

where
$\gamma$ = $\frac{C_P}{C_V}$ = specific heat at constant pressure $C_P$ over specific heat at constant volume $C_V$ for the gas
$K$ = $P_iV_i^\gamma$
$P_i$ = initial pressure before compression
$V_i$ = initial volume before compression
$V_f$ = final volume after compression

This calculator uses the equation above to give you the work done compressing the gas. For the scenario you describe of compressing 0.26 L air starting at STP (20°C, 101.3 kPa) to one eighth that volume the result is approximately 90 Joules. That is roughly the work required to lift 10 kg or 20 lbs by 1 meter— certainly on the same order of magnitude as turning a hand-crank to start an engine:

Image source: Wikimedia Commons