At the beach, atmospheric pressure is 1025 mbar. You dive
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- Consider a column of a planet's atmosphere. The planet's atmosphere is a compressible ideal gas at rest that obeys the polytropic relation Po %3D 3/2 Po 3/2 where pis pressure and pis density. Here, p, and P, are the values of pressure and density, respectively, at the planet's surface. Take z (altitude) to be positive upward with z=0 at the surface, take R to be the gas constant for the planet's atmosphere, and take g to be the downward acceleration due to gravity. a) Starting from hydrostatic balance and the polytropic relation above, derive an expression for the pressure field, p(z), in terms of the given parameters. Leave all parameters except the polytropic index as algebraic. b) Derive an expression for the density field, p(z), in terms of the given parameters. Leave all parameters except the polytropic index as algebraic. c) Derive an expression for the temperature field, T(z), in terms of the given parameters. Leave all parameters except the polytropic index as algebraic.arrow_forwardAs shown in the figure below, a piston-cylinder assembly contains 1 kg of water at T1=200° C and P1 = 1.5 bar holding the piston against the stops. The atmospheric pressure is 1 bar, and you can assume the piston's weight is negligible. The water is slowly cooled until the piston just begins to move downward in the cylinder. What is the pressure (P2), temperature (T2), and volume (V2) of water at this point? (°C), V2 = P2 = (m³) The cooling continues until water has entirely turned into saturated liquid. What is the pressure(P3) and temperature (T3), and volume (V3) of water at this point? (°C), V3 = P3 = (bar), T2 = (bar), T3 = Qtotal Calculate the total work done on the moving boundary of this system during the two processes. W total (kJ) Calculate the total heat transfer during the two processes. (kJ) On paper draw the P-v diagram for water going through the above processes. Show your detailed work on paper. hint: you must also find v1, u1, and u3. Patm = 1 bar Piston (m³) Stopsarrow_forwardA fluid has a specific weight of 132.44 kN/m3. Find its density in kgm/m3 and lbm/ft3, specific gravity, and its specific volume m3/kgarrow_forward
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