. Air is contained in a piston-cylinder apparatus, as shown in Figure 1 below. The cylinder contains stops which limit the movement of the piston between the upper and lower volumes of
0.6 and 0.2 m3
, respectively. The piston may be considered frictionless and “floats” in between
the stops when the pressure is 500 kPa. Initially, 3.66 kg of air at a temperature of 127 oC and
volume of 0.6 m3
is contained in the cylinder. The air is then slowly cooled until the volume drops
to one-half its initial value.
(a) What is the initial pressure (kPa) of the air? State any assumptions made. (15 points)
(b) What is the final pressure (kPa) of the air? (10 points)
(c) What is the final temperature (oC) of the air? (10 points)
(d) How much work is done during the process? (Hint: When pressure moves from P1 to P2, this
is done at constant volume and then the volume decreases to V2 at constant P2) (15 points)
(e) Calculate the heat transfer during the process and comment on the answer. (10 points)
(f) BONUS: Sketch the PV diagram for this process and indicate the work done. (10 points)
Figure 1: Piston –cylinder apparatus (not drawn to scale)

Astate of matter all that has define volume and can flow is a(n)

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?

(2) (a) you have a simple circuit that consists of only a battery (δvbat=1.5v) and two resistors with resistance r1=10ω and r2=5ω, connected in series with each other. what is the current running through the battery? (b) you re-arrange your circuit so now r2 is attached in parallel to r1 rather than in series. what is the current running through the battery? (c) you add an additional resistor r3=7ω on the same branch as r2. what is the current running through the battery? (d) what is the power dissipated in r3?