# Homework #1 MEMS 0051 – Introduction to Thermodynamics solved

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## Description

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Problem #1
Use the phase diagram of water (Fig. 3.7 on page 54 of Sonntag 7e) to determine the phase of water at the following
conditions. Sketch the phase diagram, including axis and region labels, and indicate where points (a)-(f) lie.
(a) 100 ◦C, 101.3 [kPa]
(b) 180 ◦C, 2,000 [kPa]
(c) 160 ◦C, 400 [kPa]
(d) 400 ◦C, 200 [kPa]
(e) 133.5 ◦C, 300 [kPa]
(f) 100 ◦C, 800 [kPa]
Problem #2
Water vapor at 200 [kPa], which has a specific volume of 0.88573 [m3/kg], is contained in a piston-cylinder device.
At this initial state, the piston is 0.1 [m] from the bottom of the cylinder. The water vapor is then cooled in a
constant pressure process such that final volume occupies half the initial. Determine:
(a) the final specific volume;
(b) the final mass;
(c) specify if this system is a open or closed, a control mass and/or isolated.
Problem #3
There exists a container with a volume of 10 [m3
]. This container is filled with 8 [m3
] of coarse stone, which has a
density of 1,600 [kg/m3
], 1 [m3
] of sand, which has a density of 1,442 [kg/m3
], and the rest is filled with water, which
has a density of 998 [kg/m3
]. Determine:
(a) the average specific volume;
(b) the average density.
Problem #4
Using the phase diagram of water (Fig. 3.7 on page 54 of Sonntag 7e), indicate which of the following processes occur
(melting, solidification, vaporization, condensation, sublimation and/or deposition) when going from the specified
initial to final state. Sketch the phase diagram, including axis and region labels, and indicate the initial and final
states connected by a straight line for parts (a)-(g).
(a) 225 [K] and 1 [MPa] → 400 [K] and 1 [MPa]
(b) 225 [K] and 0.0001 [MPa] → 400 [K] and 0.0001 [MPa]
(c) 500 [K] and 10,000 [MPa] → 500 [K] and 100 [MPa]
(d) 500 [K] and 0.1 [MPa] → 350 [K] and 10 [MPa]
(e) 225 [K] and 0.01 [MPa] → 400 [K] and 0.1 [MPa]
(f) 525 [K] and 100 [MPa] → 525 [K] and 10,000 [MPa]
(g) 300 [K] and 0.0001 [MPa] → 225 [K] and 0.0001 [MPa]
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