Question

Problem 3 (30 points) A vertical piston-cylinder assembly, as shown in the diagram, contains a given gas. The piston has a mass of 100 kg and the surface area of the piston is 0.025 m². The gas is heated slowly from an initial volume of $V_1$ = 0.01 m³ to a final volume of $V_2$ = 0.03 m³. The spring force varies linearly from zero when the volume is 0.01 m³ 1000 N when the volume is 0.03 m³. The local acceleration of gravity is 9.81 m/s² and the atmospheric pressure is 100 kPa. The internal energies at states 1 and 2 are $U_1$ = 100 kJ and $U_2$ = 250 kJ, respectively. a) On a free body diagram show the forces acting on the bottom surface of the piston at an arbitrary position $z$ measured from the bottom of the cylinder. b) Derive an expression for the absolute pressure of gas a function of $V$ in the range of $V_1$ ? $V$ ? $V_2$. c) Evaluate the pressure of the gas, in bar, at initial and final states. d) Evaluate the work done by the gas during this process. e) Determine the heat transfer during the process in kJ. f) Use a computer software (IT, EXCEL, etc.), to generate data for the absolute pressure of gas from $V_1$= 0.01 m³ to $V_2$=0.03 m³, at interval of 0.002 m³. Provide a computer generated p-V diagram for the process.

          Problem 3 (30 points)
A vertical piston-cylinder assembly, as shown in the diagram, contains
a given gas. The piston has a mass of 100 kg and the surface area of
the piston is 0.025 m². The gas is heated slowly from an initial volume
of $V_1$ = 0.01 m³ to a final volume of $V_2$ = 0.03 m³. The spring force
varies linearly from zero when the volume is 0.01 m³ 1000 N when
the volume is 0.03 m³. The local acceleration of gravity is 9.81 m/s²
and the atmospheric pressure is 100 kPa. The internal energies at
states 1 and 2 are $U_1$ = 100 kJ and $U_2$ = 250 kJ, respectively.
a) On a free body diagram show the forces acting on the bottom
surface of the piston at an arbitrary position $z$ measured from the
bottom of the cylinder.
b) Derive an expression for the absolute pressure of gas a function of
$V$ in the range of $V_1$ ? $V$ ? $V_2$.
c) Evaluate the pressure of the gas, in bar, at initial and final states.
d) Evaluate the work done by the gas during this process.
e) Determine the heat transfer during the process in kJ.
f) Use a computer software (IT, EXCEL, etc.), to generate data for
the absolute pressure of gas from $V_1$= 0.01 m³ to $V_2$=0.03 m³, at
interval of 0.002 m³. Provide a computer generated p-V diagram
for the process.

Problem 3 (30 points)
A vertical piston-cylinder assembly, as shown in the diagram, contains
a given gas. The piston has a mass of 100 kg and the surface area of
the piston is 0.025 m². The gas is heated slowly from an initial volume
of V1 = 0.01 m³ to a final volume of V2 = 0.03 m³. The spring force
varies linearly from zero when the volume is 0.01 m³ 1000 N when
the volume is 0.03 m³. The local acceleration of gravity is 9.81 m/s²
and the atmospheric pressure is 100 kPa. The internal energies at
states 1 and 2 are U1 = 100 kJ and U2 = 250 kJ, respectively.
a) On a free body diagram show the forces acting on the bottom
surface of the piston at an arbitrary position z measured from the
bottom of the cylinder.
b) Derive an expression for the absolute pressure of gas a function of
V in the range of V1 ? V ? V2.
c) Evaluate the pressure of the gas, in bar, at initial and final states.
d) Evaluate the work done by the gas during this process.
e) Determine the heat transfer during the process in kJ.
f) Use a computer software (IT, EXCEL, etc.), to generate data for
the absolute pressure of gas from V1= 0.01 m³ to V2=0.03 m³, at
interval of 0.002 m³. Provide a computer generated p-V diagram
for the process.

Added by Albert B.

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