- #1
T C
- 387
- 10
- TL;DR
- I am describing here a thought experiment where power consumption for expanding and compressing has been compared side by side to find out which one consumes more energy.
I want to share a thought experiment here. Suppose, we have a cylinder with a frictionless piston added to it. Enclosed in it is 1 gm-mole of a diatomic gas at 1 kg/cm^2 pressure and having volume of 0.0224 m^3. The temperature is 27°C i.e. 300°K.
Now, in the first scenario, the gas has been expanded adiabatically by pulling the piston outwards and the volume have been increased to 0.0672 m^3 i.e. three times to its initial volume. As the process is adiabatic, the temperature will fall to -80°C or 193.2°K. That's the temperature of the gas after expansion.
Now, in this scenario, without going into complex equations, we can assume that the cylinder is being pushed against atmospheric pressure i.e. 1 kg/cm^2. We know that the increase in volume and by multiplying both, the amount of energy consumed in the process has been found to be 448 J. and, kindly note that this is the highest amount of energy consumption. Actually the power consumption would be less as the pressure inside isn’t zero but will gradually decrease. But, for the sake of simplicity, let’s consider the power consumption to be this for now.
Now, in the second scenario, the same gas has been compressed to 1/3rd of its original volume. In that case, the temperature will rise to 465.54°K or 192.39°C. The power consumption is 3440 J in the whole process. Now, the hot has been cooled to 27°C i.e. 300°K and is being released to atmospheric pressure i.e. 1 kg/cm^2 pressure. The fall in temperature in that case would be the same as the first scenario as described before i.e. -80°C or 193.2°K. That's the temperature of the gas after being released.
In short, we get the same level of cooling with both the cases. But in the first case, the power consumption would be much less in comparison to the second. Want to know others opinions in this regards.
Now, in the first scenario, the gas has been expanded adiabatically by pulling the piston outwards and the volume have been increased to 0.0672 m^3 i.e. three times to its initial volume. As the process is adiabatic, the temperature will fall to -80°C or 193.2°K. That's the temperature of the gas after expansion.
Now, in this scenario, without going into complex equations, we can assume that the cylinder is being pushed against atmospheric pressure i.e. 1 kg/cm^2. We know that the increase in volume and by multiplying both, the amount of energy consumed in the process has been found to be 448 J. and, kindly note that this is the highest amount of energy consumption. Actually the power consumption would be less as the pressure inside isn’t zero but will gradually decrease. But, for the sake of simplicity, let’s consider the power consumption to be this for now.
Now, in the second scenario, the same gas has been compressed to 1/3rd of its original volume. In that case, the temperature will rise to 465.54°K or 192.39°C. The power consumption is 3440 J in the whole process. Now, the hot has been cooled to 27°C i.e. 300°K and is being released to atmospheric pressure i.e. 1 kg/cm^2 pressure. The fall in temperature in that case would be the same as the first scenario as described before i.e. -80°C or 193.2°K. That's the temperature of the gas after being released.
In short, we get the same level of cooling with both the cases. But in the first case, the power consumption would be much less in comparison to the second. Want to know others opinions in this regards.