To determine how much energy is needed from the chemical energy store of the coal, we need to consider the efficiency of both the electric car and the coal power station.
First, let's find out how much energy is required at the power station to provide the electric car with 100 J of useful energy. We know the electric car is 85% efficient, so:
Energy at the power station = Useful energy (in the car) / Efficiency (of the car)
Energy at the power station = 100 J / 0.85
Energy at the power station ≈ 117.65 J
Now that we know how much energy is needed at the power station, we can determine how much chemical energy from the coal is required to generate that amount. The coal power station has an efficiency of 35%, so:
Energy from the coal = Energy at the power station / Efficiency (of the coal power station)
Energy from the coal = 117.65 J / 0.35
Energy from the coal ≈ 336.14 J
Therefore, 336.14 J of energy is needed from the chemical energy store of the coal for the electric car to provide 100 J of useful energy.