A gasoline motor lifts a 25N block a distance of 10m. The total amount of energy used by the motor is 750 J. How much energy does the motor convert to heat?
We can use thermodynamic equations to solve this problem.
We consider the engine to be a thermodynamic system. Thermodynamic systems evaluate the energy going into and out of a particular environment. We consider energy flow out of the system to have a negative value, and energy going in to be positive.
The equation U = Q + W is used to represent this energy flow.
U = the change in energy of the system
Q = heat
W = work
Some amount of energy is always converted to heat instead of work as it leaves the system; this is why no engine is 100% efficient.
In this case, we need to find Q.
We know that U = 750J
We know that W = Fd
So 750 = Q + 25(10)
750 = Q + 250
Q = 500J
(We should note that it would actually take slightly more than 25N of force to accelerate the block from a resting position, as a force of 25N would only match the force of gravity and hold the block in place. However, since we are not told the velocity, time or acceleration, it is not possible to determine what this force is.)