You are working for a grain storage company over the summer, and they have a pro

Question

You are working for a grain storage company over the summer, and they have a problem with the grain elevator, which keeps breaking down. The morning, your boss woke up feeling like a genius and decides that he is going to design one on his own, so he gathers the engineering group in his office to explain idea. The projected elevator consists of a platform mounted on a piston that can move along a cylinder. The cylinder is open to the room at the top. The lower part of the cylinder is also full of air, but the tight fitting piston seals this chamber, so that no air can escape. The piston has a cross-sectional area of 9.8 m^2. Initially the elevator is unloaded and the air inside the air chamber starts at room temperature (25 degree C) and a pressure of 120 kPa. 20 metric tons of grain are loaded on the platform. During the loading process, the temperature of the gas remains at 25 degree C, and the piston sinks as the pressure increases. After loading is done, the air in the chamber is then heated up to 125 degree C, and the elevator rises slowly and steadily. The pressure remains constant. The elevator is unloaded; the gas is cooled during this process in such a way that the height of the piston remains constant. Finally, the air is cooled back to room temperature, and the piston returns to its starting level. The pressure remains constant. You need to convince your boss that this is a very inefficient system. You may assume that the gas is diatomic.

Explanation / Answer

Assume ideal condition means there is no energy loss in system

I well explane whole working process mathematically

WE KNOW

PV= n RT

in step A

T= 25 C P= 120 Kpa

n will be always constent because chamber is air tight

when we will load a 20 tonn of grain pressure will increase if T constent then

according to PV= n RT , V will decrease and piston will go down

in step B

if we are heating the chamber means increasing the temprature T and given that Pressure is constent

then according to PV= n RT if T increasing and P= constent

V will increase thats why piston will go up wery slow.

an step C

when elevater is unloaded when we unloading we can cool chember

means T and P are decreasing

so PV= n RT

when T and P both are decreasing we have to adjust the rate of cooling such that V= constent

then in step D

Finally if there is no energy loss and you are bringing chamber back to room temprature then whole system will be at initial state.

only we have to do is to heat and coool the chamber in control mannert hence it is very efficent process .

Thanks

for any query plz comment

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