3. (2016 Midterm) Consider as a system the gas in the cylinder shown in the following figure: the cylinder is fitted with a
piston on which a number of small weights are placed. The initial pressure is 200 kPa and the initial volume of the gas is 0.04
m3 .
(a) Let a burner be placed under the cylinder and let the volume of the gas increase to 0.1 𝑚3 because of heating from the
burner. Calculate the work done by the system during this process. (Hint: In this case, the pressure remains constant)
(b) Consider the same system and initial conditions. At the same time, the burner is heating under the cylinder and the piston
is rising. However, in this case, the weights are removed from the piston at such a rate that the temperature of the gas remains
constant. (Hint: Assume ideal gas)
(c) Consider the system and initial state given in the first two examples, but let the piston be held by a pin so that the volume
remains constant. In addition, let heat be transferred to the system until the pressure increases to 300k Pa. Calculate the work.
4. (2016 Midterm) A piston whose mass is 1000 kg is initially held in place by a removable latch as shown in the figure below.
The cylinder is oriented vertically and its cross-sectional area is constant at 0.1 𝑚2 . The initial volume of the gas in the
cylinder is 0.5 𝑚3 and the pressure is 1 MPa. The working fluid may
be assumed to obey the ideal gas equation of state. The cylinder has a
total volume of 1 𝑚3 and the top end is open to the surrounding
atmosphere at pressure 101 kPa. When the latches are removed the
piston rises through the cylinder without any friction and is then
ejected from the cylinder through the top (see figure below). In
addition, by fast heat transfer, the gas in the cylinder is always kept at
the same temperature.
(a) What will be the velocity of the piston as it leaves the cylinder?
(b) What will be the heat transfer from the cylinder during this process?
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