Gasdynamics Assignment 1 — Review of Thermodynamics
Write your solutions in single column format, with one statement following another vertically. Write your solutions neatly so that they are easy to read and verify. Don't write one line with two equal signs. Make sure your answers are clearly highlighted using a box followed by the “A” symbol. Failure to do this will result in points getting deducted.
 01.31.22
 Question #1
A totally enclosed cylinder is perfectly insulated thermally around its side and one end and contains a frictionless thermally non-conducting piston:
The other end of the cylinder is perfectly conducting thermally. Initially, each side of the piston contains 0.0283 m$^3$ of air and 0.0283 m$^3$ of argon, respectively at 21$^\circ$C and $103$ kN/m$^2$. The argon side is completely insulated. If by adding heat to the air side the argon is compressed until its pressure reaches 206 kN/m$^2$:
 (a) What is the internal energy change of the argon? (b) How much heat was transferred to the air?
 12.29.22
 Question #3
A rigid nonconducting tank with a volume of $120$ cubic meters is divided into two equal parts by a thin membrane. Hydrogen gas is contained on one side of the membrane at $3.5$ bar and 80$^\circ$C. The other side is a perfect vacuum. The membrane is suddenly ruptured, and the H$_2$ gas fills the tank following the polytropic process $P V^{1.2}={\rm constant}$. What is the entropy change of the hydrogen? Consider hydrogen to be a perfect gas ($R=4.124$ kJ/kgK, $c_p=14.307$ kJ/kgK, $c_v=10.183$ kJ/kgK).
 01.10.23
 Question #4
In a gas turbine engine, the combustion products are expanded to ambient pressure through a nozzle as follows:
The gas constant and the specific heat at constant pressure of the combustion products is of $415$ J/kgK and of $1800$ J/kgK respectively and can be taken as constant throughout the nozzle. The properties at the nozzle entrance are as follows: $P_1=10$ bar, $T_1=2000$ K, $v_1=40$ m/s. Knowing that friction induces a change in specific entropy between the nozzle exit and entrance of $s_2-s_1=264.6$ J/kgK and that the pressure at the nozzle exit corresponds to $P_2=1$ bar, do the following:
 (a) Find the polytropic coefficient $n$ for this process (recall the polytropic relationship $P/\rho^n={\rm constant}$). (b) Which common thermodynamic process (isentropic, adiabatic, reversible, isochoric, isobaric, etc) is closest to the process taking place in the nozzle? (c) For cross-sectional areas at the nozzle entrance and exit equal to $A_1=1$ m$^2$ and $A_2=0.9$ m$^2$ respectively, determine the flow speed at the nozzle exit.
 01.17.23
 Question #5
Consider a cylinder in which a piston made of steel separates air and helium as follows:
Knowing that the gravitational constant $g=9.81$ m/s$^2$, that the temperature of both gases is of 44$^\circ$C, that the radius of the cylinder is $R=0.1$ m, that the length of the cylinder $L=1$ m, that the mass of the piston is of 25.29 kg, that the density of the steel is of 8050 kg/m$^3$, and that the mass of the air and of the helium is of 0.0003 kg and of 0.00003 kg respectively, find $L_{\rm A}$.
 $\pi$