In the steam driven jack system shown in the figure, a vehicle with a mass of $2$ tons is to be lifted $1$ meter above the horizontal position. Initially, there is $10$ liters of water in the tank at $25$ C$.$ The piston diameter is $10$ cm $.$

a$)$ Considering that the cylinder is heated from its upper surface by means of a flame, find the amount of heat required for this process.

b$)$ Find how many kg of fuel should be consumed when heating is provided with a fuel with a lower calorific value of $H=44000k\frac{J}{k}g$ and the combustion efficiency is assumed to be $100\%.$