Suppose that an internal combustion engine runs on octane, forwhich the enthalpy

Question

Suppose that an internal combustion engine runs on octane, forwhich the enthalpy of combustion is -5512kJ mol^-1 and take themass of 1 gallon of fuel as 3kg. What is the maximum height,neglecting all forms of friction, to which a car of mass 1000kg canbe driven on 1.00 gallon of fuel given that the engine cylindertemperature is 2000 degrees C and exit temperature is 800 degreesC? Please show work. I have no idea where to start. Suppose that an internal combustion engine runs on octane, forwhich the enthalpy of combustion is -5512kJ mol^-1 and take themass of 1 gallon of fuel as 3kg. What is the maximum height,neglecting all forms of friction, to which a car of mass 1000kg canbe driven on 1.00 gallon of fuel given that the engine cylindertemperature is 2000 degrees C and exit temperature is 800 degreesC? Please show work. I have no idea where to start.

Explanation / Answer

Given: 1gallon of fuel (octane) = 3kg We know, moles = mass / molar mass So 3kg of octane = 3kg (1000g /1kg) / (114.23g/mol) =26.26mol Heat released when 3kg of octane is completely burned =5512kJ/mol * 26.26mol = 144745.12kJ We know, efficiency, = w / q So, work done, w = q                              = (1 - (800 /2000))* 144745.12kJ                              = 0.6 * 144745.12kJ                              = 86847.072kJ We know that, work done = mgh So 86847.072kJ (1000J /1kJ) = 1000kg * 9.8m/s^2 *h          86847072J = 9800kgm/s^2*h          h =86847072J /9800kgm/s^2                = 86847072kgm^2/s^2 / ( 9800kgm/s^2)                =8861.95m Hence, car can be driven to 8861.95m Hence, car can be driven to 8861.95m

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