Question

Fluid Mechanics

The figure below shows a piston-cylinder assembly, initially in static equilibrium. Inside the assembly there is pressurized gas with a gauge pressure equal to 150 kPa. If the piston diameter is 0.1 m and the surrounding atmospheric pressure is 100 kPa. Assume that no gas leaks through the interface of the piston and cylinder surfaces and there is no friction between surfaces. Please answer the following.

a. For the initial conditions, the gas and the surroundings have the same temperature. Determine the weight of the piston such that the initial condition of static equilibrium is satisfied. Start your solution by defining a suitable boundary for the gas and showing a free body diagram.Express your answer with a reasonable number of decimal places. In your opinion, could an average person hold the piston on one hand? Why?

b. Next, the gas receives heat and increases its temperature and volume thus lifting the piston by0.3 m while the gas pressure remains constant in a quasi-equilibrium process. Use Eqn. 2-22 of your textbook to determine the work done by the gas to lift the cylinder. Also, sketch the process on a Pressure versus Displacement diagram and on a Pressure Volume diagram. Only use symbols on your axes and associate the initial state with subscript 1 and the final state with subscript 2, i.e., the final state would have a volume V2.

Modify Eqn. 2-22 such that the independent variable is volume. How does it relate to the ketch that you created in part (b)?C.

d. Thinking about potential, kinetic, and internal energy for the gas. Would it change during the process? Explain your reasoning.

e. Assume that from the heat supplied to the air, only 60% gets transformed into work, 20% getstransformed into internal energy, and 20% is transferred to the surroundings. Create anexpression to define the efficiency of this assembly to lift the piston based on the energysupplied.


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