Suppose that the piston is now allowed to move within the cylinder, but that the

Question

Suppose that the piston is now allowed to move within the cylinder, but that the walls remain
adiabatic and impermeable so that no heat flows into the gas. The gas system will ultimately
move to a new equilibrium state. We will now characterize the final equilibrium state and the
changes resulting from the process.
Define the
(Total System) = (the gas enclosed in the cylinder) plus (the mass placed on the piston)
The internal energy, UT , for the total system then satisfies the following relation:
UT =U +Um ,
where U is the energy of the gas and Um is the gravitational potential energy of the mass.
Let us assume that this total system forms an isolated system.
c. Determine the change in the internal energy of the Total System, UT .
d. Determine the pressure of the gas at equilibrium.
e. Demonstrate that the final volume of the gas is 1.4 × 103m3 .
f. Calculate the work done on the gas, w .
g. Calculate the change in gravitational potential energy of the mass.
h. Calculate the change in internal energy of the gas.

* I dont even get how to start on these questions.. Please help me on the c.. and give he hints on others

too hard for me.. Please help me urgent help needed!

Explanation / Answer

c) you are given that UT = U + Um.

Thus, change in total internal energy = Ufinal + Um(final) - Uinitial - Uminitial = [Ufinal - Uinitial] + [Umfinal - Uminitial] = [change in Ugas] + [change in Um].

From first law of thermodynamics, change in internal energy of gas du = dQ - dW.

But dQ is 0 since there is no heat addes or removed. dW is work done which is PdV where P is pressure and dV is change in volume. But change in volume = Area x change in height = Adh where dh is change in h as piston moves up and down.

Thus, change in internal energy of gas = pAdh and if gas expands, it is negative and vice versa.

change in Um = mgdh where dh is change in height.

NOTE: depending on how advanced your course is, you might have to use a special formula for work done during adiabatic process. Check out the wikipedia article on "adiabatic process."

d) Pressure of gas x Area = Force on piston. This force must balance out the weight mg.

So pressure = mg/area of piston.

e) you know initial temperature. thus, you can find initial internal energy. in c), we calculated change in internal energy. so you can find final internal energy. thus, you can find final temperature.

initial volume + A*h. so you know intial and final temperature and initial volume. you can find final volume using equations found in the wikipedia article.

f) substitute values into the formula for work done.

g) mg dh

h) dU = dQ - dW

but in adiabatic, dQ = 0.

Thus, dU = -dW = - (answer to question (f))

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