HW #2 Key
ME 320
1.
Schematic:
Given
: 5 kg of steam inside the cylinder
Process occurs in which: Q= 80 kJ and W
shaft
=-18.5 kJ
The internal energy of the system changes from u
1
=2709.9 kJ/kg to u
2
=2659.6 kJ/kg
Assume:
Neglect kinetic and potential energy
For a closed system, the 1st law is:
Specifically for this problem, the 1st law is:
This can be rearranged for W
piston
:
Substituting values gives:
The system pushes the piston outwards to perform 350 kJ of work on the surroundings.
2.
Find:
Ideal Gas Law for 90% elastic collisions
Nomenclature
: P=pressure, F=force, A=area, p=momentum, t=time, v=velocity, v
x
= x-component of
velocity vector, L=length, N=number of particles, V=volume, m=mass, T=temperature, k=Boltzmann
constant, R=universal gas constant

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We will proceed similarly to how the derivation was done in class. Start with the equation for pressure:
so P=
The time between collisions can be expressed as:
Therefore the frequency of collisions with one wall for N particles will be ½*v
x
/L.
From this, we can get:
Next, we want to express the momentum change in terms of velocity and mass. However, first we must

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