How can the heat absorbed by an engine be measured by "measuring the fall in a weight"? In Atkin's Introduction to the thermodynamics, he speaks about the definition of the absolute thermodynamic temperature scale and in his discussion he states that the work done by any engine can in principle be measured by observing the height to which a weight of known mass is raised by the engine. This is very clear and intuitive to me. Simply hook the engine up to some mechanical device that raises a mass and you can easily calculate the work done by the engine.
He then goes onto say that the "heat absorbed by any engine can also, in principle at least, be measured by measuring the fall in a weight". This on the other hand is not very easy to understand. How can we determine the heat absorbed by measuring the fall in a weight? I can't seem to imagine any kind of mechanical contraption which would lower a mass by a distance related to the heat absorbed by the engine. Is there any way to do this in principle at least?
Any help on this issue would be most appreciated!
 A: The principle that the fall in weights can be used to measure the energy absorbed by heat follows directly from the conservation of energy for an isolated system: $$\Delta U_g + \Delta E_{int} = 0$$
The system under consideration comprises of the falling masses, the Earth and the engine. The change in gravitational potential energy $\Delta U_g$ is negative because the two masses fall, and as the system is isolated for energy, there is an associated increase in the internal energy, which is transferred by heat.
I'm not quite sure of any apparatus that uses this principle to calculate the energy absorbed by heat, but a somewhat similar design was used by the famous James Prescott Joule in determining the "mechanical equivalent of heat":

The system this time comprises of the two masses, the Earth and the insulated volume of water. The decrease in gravitational potential energy causes a consequent increase in the internal energy of the water, which is transferred by work done by the rotating handles and the increase in temperature is measured by an (external) ideal thermometer.
Hope this helps
A: 
How can we determine the heat absorbed by measuring the fall in a
weight?

Heat is not absorbed due to the fall of a weight. The purpose of the falling weight experiment is to demonstrate the equivalency between energy transfer by work and energy transfer by heat.
The fall of the weight in the diagram given by @Cross does paddle work (stirrer work) on the water increasing its internal energy as a result of fluid friction, as evidenced by the temperature rise of the water. Assuming no heat loss through the walls of the container, the increase in internal energy (increase in temperature) equals the decrease in gravitational potential energy of the weight, or
$$MC(T_{f}-T_{i})=mgh$$
The right side is the work done by the falling weight (loss of gravitational potential energy) on the water and the left side is the increase in internal energy of the water and
$M$ is the mass of the water
$T_{f}$ and $T_{i}$ are the final and initial temperatures of the water.
$C$ is the specific heat of the water
$m$ is the mass of the weight
$h$ is the height of the fall
$g$ is the acceleration due to gravity
The same increase in internal energy (same temperature increase) can be achieved by placing the container of water initially at temperature $T_i$ in a room maintained at constant temperature $T_f$ (a thermal reservoir) until the container of water comes into thermal equilibrium with the room at which point heat transfer stops. Then the heat transfer $Q$ from the room to the container of water is
$$Q=MC(T_{f}-T_{i})$$
Which establishes that the mechanical work $mgh$ is equivalent to the heat transfer $Q$, or
$$mgh=Q$$
Hope this helps.
