# Homework #1 MEMS 0051 – Introduction to Thermodynamics solved

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## Description

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Problem #1
Consider a power plant shown below. The red dashed line is the control surface (C.S.) around the cooling tower.
(a) Is the control volume (C.∀.) an open or closed system?
(b) Is the C.∀. that of an isolated system?
(c) Is the C.S. stationary or moving?
Make-up
water
Turbine
discharge
water
Power generation
station
Pump
inlet water
Problem #2
Given the Matlab script for the phase diagram of water, determine the phase(s) based upon the following properties.
Plot the phase diagram and label each state (i.e. (a), (b), (c), etc.).
(a) 250 [K] and 4·104
[MPa]
(b) 700 [K] and 1.1·104
[kPa]
(c) 273 [K] and 100 [kPa]
(d) 274 [K] and 100 [kPa]
(e) 400 [K] and 2,000 [kPa]
(f) 273.16 [K] and 600 [Pa]
(g) 373.15 [K] and 101.325 [kPa]
(h) 600 [K] and 10,000 [Pa]
(i) 750 [K] and 250 [MPa]
Problem #3
Given the P − ν diagram for the diesel cycle to the right, and based upon
the processed learned in Lecture 1, identify and label the three processes
that comprise this cycle.
P
v
1
Problem #4
Given the following list of properties, determine if they are intensive or extensive (i.e. write “intensive” or “extensive” next the corresponding number on the homework submission sheet). You may have to research a given property.
(a) Electrical conductivity
(b) Dynamic viscosity
(c) Thermal conductivity
(d) Modulus of elasticity
(e) Modulus of rigidity
(f) Dieletric strength
(g) Permeability
(h) Emissivity
(i) Boiling point
(j) Yield strength
Problem #5
1 [kg] of compressed water at 500 [kPa] and 20 ◦C has a specific volume of 0.001002 [m3/kg], is contained in a
piston-cylinder device. The water is then heated in a constant pressure process such that final volume is ten times
that of the initial volume. Determine:
(a) the final specific volume;
(b) specify if this system is a open or closed, a control mass and/or isolated.
Problem #6
There exists a container with a volume of 18.9 [L]. This container is filled with 68 [kg] of steel (ρS=7,750 [kg/m3
])
shot, with 5 [L] of sand, which has a density of 1,482 [kg/m3
], and the rest is filled with water, which has a density
of 998 [kg/m3
]. Determine:
(a) the volume-weighted average specific volume;
(b) the average density.
Problem #7
Water flows through a pipe from a high-elevation reservoir to a low-elevation reservoir purely via gravity-driven flow.
If the change of elevation between the high- and low-elevation reservoirs is 15 [m], the average velocity of the water
is 3 [m/s], and the water is at standard-temperature standard-pressure (i.e. has a specific internal energy of 104.86
[kJ/kg]), what is the total specific energy of the system with respect to the high-elevation reservoir?
Problem #8
Consider the piston-cylinder assembly shown to the right (neglecting the heads, and intake and exhaust vales). Both
intake and exhaust valves are closed. The piston starts at bottom dead center (BDC) and compresses to top dead
center (TDC). The displacement of the piston is 0.5 [L], and the compression ratio is 10.5:1. The bore diameter is
83 [mm] and the stroke length is 92 [mm]. Assume that the fluid, which is air, has been given sufficient time to
compress. If it takes 5.5 [kN] to compress the air, i.e. move the piston from BDC to TDC, answer the following:
(a) Determine the internal pressure of the fluid after compression, assuming the initial pressure was
101.352 [kPa];
(b) What happens if the diameter of the pistoncylinder assembly is halved?
(c) Can you assume quasi-static equilibrium throughout the fluid during compression? Explain.
(d) Did the fluid undergo a process or a cycle? Explain.
(e) Is the fluid an isolated system during this compression? Explain.
P
BDC
TDC
2