Physics 230 Homework Set 4 solved

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CQ1. Imagine you have two containers of equal amounts of oxygen gas at initially equal
temperatures. You then supply equal amounts of heat to each container. The first
container undergoes an isobaric contraction and the second container undergoes an
isochoric cooling. After each container was heated, which has the higher final
temperature? Your explanation needs to include the first law of thermodynamics.

CQ2. Knight: Conceptual Questions 9

CQ3. Knight: Conceptual Questions 11
P1. A cylinder with an initial volume of 3.60 ⇥103 cm3 holds 0.100 mol of oxygen gas at
120.C. The gas is expanded by a piston to a final volume of 5.40 ⇥103 cm3. How
much work was done on this gas if this process was done at
a) constant pressure and
b) constant temperature?

P2. Reconsider the isobaric and isothermal processes outlined in the previous problem.
For the isobaric process…
a) i. What is the change in thermal energy of the diatomic gas?
ii. What is the heat added or removed from the gas?
For the isothermal process…

b) i. What is the change in thermal energy of the diatomic gas?
ii. What is the heat added or removed from the gas?

P3. Consider the cylinder of Figure 17.13 that contains a gas that undergoes an isobaric
expansion.
a) Draw a pV diagram showing this process. This diagram needs to include axes
labels and an arrow indicating the direction traversed between the initial and final
points on the pV curve.

b) Describe a series of steps to implement this ideal-gas process.
c) Show the process as a first-law bar chart.

P4. Imagine two ice cubes, each with a mass of 55 grams and an initial temperature of
-14.0C. The ice cubes are dropped into 220 grams of water, which has an initial
temperature of 26.0C and is in a thermally insulated container.
a) What is the final temperature of the beverage once equilibrium is reached?
b) What is the final temperature if only one ice cube is used?

P5. Consider a scenario where an unknown mass of 100C steam is mixed with 210 g of ice,
which is at its melting point. The mixing occurs in a thermally insulated container.
After thermal equilibrium is reached, the liquid is found to have a temperature of 55C.
Calculate the unknown mass of the steam.

Extra Credit Problem (+12 points):
P6. Consider a sample of oxygen gas, which has a mass of M = 1.88 g, that starts at an
initial state A as indicated in the attached figure. The gas undergoes an isobaric
expansion to a state B, then an isochoric heating, bringing the gas to state C
Lastly, the gas returns to state A via the path indicated in the attached figure.
a) Calculate the temperature of the gas in Kelvin when the gas is described by states
A, B, and C, respectively.
b) Calculate the heat, Q, work done on the gas, W, and thermal energy change, Eth
for the gas as it goes through each of the three aforementioned processes.

Notice: for the state C to state A process, integration must be used!
2
p (x 105 Pa)
V (x 10-3 m3)
1.0 2.0 3.0 4.0
1.0
2.0
3.0
4.0
A B
C
Figure 1: Pressure vs volume plot