I need help with this riding lawn mower problem. Give the operating temperatures

Question

I need help with this riding lawn mower problem. Give the operating temperatures and efficiency, compute the work per cycle of the gasoline enginer and determine the amount of gasoline, in gallons, required to operate the gas mower for 2.8 hours. You can assume that all energy liberated in burning the fuel goes into Qh and that gasoline has an energy density of 46.4 MJ/kg.

Ariens 42 in 17hp riding mower spec Value Mass with rider 260kg Rear wheel radius 20cm Gas engine power 17hp Gas engine max temp 877k Ambient temp 293k Gas engine efficiency 0.5 of Carnot Gas engine RPM 1500RPM Two cutting DC motors, power, each 500W Cutter blade RPM 1000RPM Cutter blade radius 20cm Runtime requirement, hours 2.8hours 1.440 kWh battery mass 27kg Max speed required 3m/s Estimated coefficient of friction while mowing 0.1

Explanation / Answer

Power Required to operate the mower    = friction coefficient * weight * velocity

                                                           = 0.1 * (260 + 27) * 9.8 * 3   = 843.78 W

Power Required to operate the cutting motor    = 2 * 500   = 1000 W

Total power required   = 1843.78 W

Efficiency of gas engine = 0.5 * ( 1   - 293 / 877)   = 33.3 %

power input to engine   = 1843.78 / efficiency    =   5537.6543 W

mass of gasoline * 46400000    = 5537.6543 * 2.8 * 3600

mass of gasoline   = 1.203 kg

volume of gasoline = 1.203 / 719.7   = 0.0016715 m^3 or 0.44156 gallons

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