# Homework #5 MEMS 0051 – Introduction to Thermodynamics solved

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Problem #1
Two rigid tanks are initially in thermodynamic equilibrium. The first tank is 0.5 [m] tall and sufficiently
insulated, and contains 5 [kg] of carbon dioxide at 80 ◦C and a pressure of 200 [kPa]. The second tank is
0.25 [m] in diameter and not insulated, and contains 10 [kg] of argon at 25 ◦C and a pressure of 500 [kPa].
The two tanks are connected by a rigid piping system that contains a valve, which is then opened. After
an extended period of time (assuming sufficiently long to achieve thermodynamic equilibrium internally and
thermal equilibrium with the environment, which is 25◦C), determine:
A The final pressure (i.e. mechanical equilibrium pressure).
B The heat transferred into our out of the tank system.
Problem #2
For the following scenarios, determine the amount of heat transfer.
A Heating a 2 [kg], 0.1 [m] long copper bar from 25◦C to 100◦C.
B 1,000 [kg] of asphalt cooling from 50◦C to 20◦C.
C The heating of 1 [kg] of oxygen in a mass-less piston-cylinder from 300 to 1,500 K.
D A piston-cylinder containing 0.1695 [kg] of nitrogen at 150 [kPa] and 25◦C that is isothermally compressed to 1.0 [MPa], which requires 20 [kJ] of work.
Problem #3
Given the system below, where a heat pump transfers heat from a low-temperature infinite reservoir (the
ocean) and transfers heat to a high-temperature infinite reservoir (say a room). The work powering the
heat pump comes from a heat engine, which accepts heat from the same high-temperature reservoir. Is
this configuration acceptable (i.e. does not violate the Kelvin-Planck and/or Clausius statements, nor is a
perpetual motion machine of the 1st, 2nd and 3rd kind)?
1
Problem #4
Two heat engines that operate in series (i.e. Q˙ H enters HE1 which rejects Q˙ M, which is the input into
HE2, which rejects Q˙ L) between a high-temperature reservoir TH and a low-temperature reservoir TL. HE1
produces work W˙
1 and HE2 produces work W˙
2. Find the efficiency of each heat engine, and the efficiency
of the overall system.
Problem #5
A heat engine operates between a high-temperature reservoir TH1 and a low-temperature reservoir Tambient.
The work produced, W˙
1, which is the difference of heat input Q˙ H1 and heat rejected Q˙ L1, powers a heat
pump. Part of the work from the heat engine enters the heat pump W˙
2, whereas the difference between

1 and W˙
2 is designated as the net work, W˙
net. The heat pump accepts heat Q˙ L2 from the same lowtemperature reservoir (Tambient) and rejects heat Q˙ H2 to a secondary high-temperature reservoir TH2. Assuming TH1=TH2>Tambient, determine, based upon the following cases (a-c), if this system satisfies the First
Law and/or violates the Second Law. Then, assuming TH1>TH2>Tambient, determine if this system satisfies
the First Law and/or violates the Second Law.
Q˙ H1 Q˙ L1 W˙
1 Q˙ H2 Q˙ L2 W˙
2
a 6 4 2 3 2 1
b 6 4 2 5 4 1
c 3 2 1 4 3 1
2