Question

14) Suppose a low-boiling liquid like ammonia is placed in a heat reservoir and part of the energy of the surroundings is used to vaporize the liquid.The adiabatically expanding gas does work by driving a piston and during the expansion the gas cools until it condenses to a liquid, the liquid is once again vaporized using energy available from the surroundings, and the cycle is repeated. Can such an engine be made operational?

Answer 1

Adiabatic expansion or compression of a gas means that the temperature of the gas changes due to change in pressure or volume of gas without actual heat lost or gained from the sorroundings. In case of expansion the temperature of the gas decreases and in case of compression the temperature of gas increases.

In other words, we can also say that Pressure X Volume = constant. Adiabatically expanding gas can never do work without loosing its internal energy.

In all combustion engines, the work is always done by the expanding gas adiabatically and thus gas looses energy. In this case a low boiling point liquid takes heat from the sorroundings and expands in a cylider with a piston and does work by moving a piston. But to consider it cools down in the engine is not physically possible reason being work done in adiabatic expansion= pressure X change in volume.

Thus, in case of work done adiabatically the gas would do work and lose its heat upto only that point where its volume increases, decrease in volume or liquefication will lead to negative work done as volume decreases in that case. Thus liquefication in this case needs either the heat to be transferred to another system by non-adiabatic means or pressure be applied for cooling and decrease in volume leads to negative work done.

So, a heat sink is required to cool the gas again to liquid state and then again it can be heated from surroundings to move piston again. But in practical cases ammonia has a boiling point of -33.4 C which in itself is difficult to achieve, thus heatsink is difficult to make.

Also, if we consider the ideal situation given above the gas does work upto point where it expand to the maximum expansion possible considering the pressure outside is p1 then if the gas does looses all its energy till it comes to pressure p1 and increases its volume then there is no work possible beyond that point. And in all practical cases the pressure required by the gas to achieve any meaningful work would be larger than p1 as other forces like friction are there to overcome. In practical cases p1 will be atmosphereic pressure and temperature lower than room temperature upto the point of work done but never lower than the boiling point of ammonia. Thus, gas left over in piston will only heat up by heat from the surrounding not cool down. That's why such an engine cannot be operational.