An engineer has developed the following idea to generate endless power anywhere
ID: 1718854 • Letter: A
Question
An engineer has developed the following idea to generate endless power anywhere in the world. First, helium-filled balloons are tethered to the ground so they remain at an altitude of 3000 m, where the standard temperature is -4.5°C, pressure 70.12 kPa. A lightweight, insulated duct is hung from those balloons so it brings that air down to sea level, where the standard temperature is 15°C, and pressure 101.33 kPa. His idea is that the cooler air inside the duct will weigh more than the outside air, so that the pressure at the bottom will be higher than outside, and thus power can be produced by simply expanding the air. You are asked to evaluate the potential to produce useful electrical power, by kg of air taken at the top, under two assumptions: (1) all the exergy of the air can be converted into electricity, by whatever means, (2) power is produced by this professor’s method, that is, by expansion of the air, which has been adiabatically compressed by gravity as it comes down the duct.
Explanation / Answer
The idea looks like a Perpetual Motion Machine. Which can not produce continuous power on its own.
Let us see how.
For Air to flow from the height of 3000 m to sea level through the duct, pressure differential is required between entry and exit of the duct. The pressure differentilal is in the reverse direction i.e. it will pull air from the bottom of the duct upwards. This rising column of air through the duct will meet cooler air at the top the duct. The heat will transfer through the air column and upper part of the air column will start cooling. The temperature of the air column inside the duct will start attaining the temperature gradiant same as that of air outside the duct. So the temperature of air inside and outside the duct at any height between sea level to 3000m will remain same. Due to this the air column in the duct will attain equilibrium and there will be no air flow through the duct. Hence there will be no power produced.