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The

It is proposed to construct an elevator to operate in consequence of successive heating and cooling of air, the working substance. The apparatus will consist of a piston and cylinder. **Figure 1** shows the intended elevator dimensions and specifications.

By inspection of the schematic we understand elevator operation will be five steps. A p-V diagram for the air is needed. States of the air are determined as the p-V diagram is sketched: **Figure 2.**

♦ **Preheat: States (1) to (2):** The elevator is charged with air initially in equilbrium with ambient surroundings (298K, 100kPa, 30m³). The piston mass and area are 230kg and 0.44m³. Therefore (by Newton's 2nd Law) the air must have the pressure p_{4} = 5,228 kPa before the piston will start to rise.

To calculate the heat (1) to (2) we require temperature, T_{2}:

Preheat happens at constant volume hence work is zero. The energy equation is:

This brings us to **State (2)** (35kg, 30m³, 5,228kPa, 15,576K), the first state of intended cyclic operation of the elevator.

♦ **Heat to Commence Lift: States (2) to (3)** The air must attain pressure sufficient to lift the piston and casting. For pressure use the 2nd Law.

At state (3), assume air is an ideal gas so:

Heat the "Heat to Commence" is:

♦ **Heat of Lift: States (3) to (4)** The volume of air will increase to 32.64m³ as the air pressure remains constant. Thus we know the conditions of State (4) (30kg, 32.64³, 27,523kPa and T = T_{4}. We might calculate W_{3-4} independently. However let's apply the energy
equation and obtain work and heat together.

The return cycle has Steps, "Cool to commence movement downward ((4)-(5))" then "Cooling to move downward to Level 1 ((5)-(6)). These events, "reverses" of the above are not analyzed here.

Knowing geometry

Premise presently unwritted!