Multiple Choice
Wintry Thermodynamics
P-V Diagrams
Perfectly Insulated Piston
100
Given two identical containers 1 and 2 with moveable tight pistons, each containing the same number of moles of the same ideal gas at the same initial volume and temperature. Both gases are then allowed to expand to the same multiple of their initial volumes. If that process is adiabatic for gas 1 and isothermal for gas 2, which gas has the larger final pressure? (A) gas 1, (B) gas 2, (C) both have the same pressure, (D) the answer depends on the initial temperature.
B
100
While on a polar expedition you erect a tent, the walls of which are unstretchable and unbendable and made of thermally insulating material. Suppose the tent holds a volume of 10m^3. The temperature inside the tent as well as outside, equals −23C (brrrrr), and the atmospheric pressure equals 1.0 atm. Use the ideal-gas equation to find the approximate number of moles of air in the tent.
About 500 Mols!
100
Let T1 denote the temperature of the gas in state (a). Express T1 in terms of n, R, p1 and V1.
T1 = P1*V1/n*R
100
Prove that the equilibrium position of the piston is at x=L/2. Ignore the thickness of the piston.
See solution on board!
200
Consider a laboratory rat which turns the wheel of a treadmill around which a string is wound which lifts a weight in the process. Treating the rat as a thermodynamic system, which of the following statements is valid? (A)Q= 0, (B)W= 0, (C)Q−∆U >0, (D) The rat cannot be treated as a thermodynamic system because it is not thermally insulated from its surroundings.
C
200
Imagine an igloo was filled with 15kg of air (M=30g/mol) which started at -23 C. With the tent sealed airtight, you run a heater until the air inside the tent reaches a balmy 27 C. (i)If the heater delivers 300 Watts of power, how long does that process take?
1731s or about 30 minutes
200
Fill in the table below. Express all pressures in terms of p1, all volumes in terms of V1, and all temperatures in terms of T1. state p V T a p1 V1 T1 b c d
state | p |V |T a |p1 |V1 |T1 b |p1/2 |V1 |T1/2 c |p1/(2)^(8/3) |2*V1 |T1/((2)^(5/3) d |p1/2 |2*V1 |T1
200
What is the equilibrium pressure of the diatomic gas? Give your answers in terms of any of L, A, T1, n, and R.
P = 2nRT1/L*A
300
A refrigerator which requires 40J of work input while expelling 120J of heat into its surroundings during each cycle, has a coefficient of performance of (A)3.0, (B) 2.5, (C) 2.0, (D) 1.0, (E) 0.5, (F)0.4, (G) 0.33.
A
300
It feels stuffy in your igloo. If your airtight, 10m^3 igloo contained air which was heated from -23C to 27C and was initially at atmospheric pressure, what is the change in pressure inside your igloo caused by the heating?
~ 0.2 atm
300
Fill in the table below. Find ALL quantities in “units” of p1V1, and enter in the table only the respective coefficient. (For example, if you find some quantity to equal −(3/2)p1V1 then enter “−1.5”.) Before you start calculating, enter “0”, “+”, and “−” for those quantities which you know to be zero, positive, or negative. step Q ? U W a-> b b-> c c-> d d-> a
step Q ? U W a-> b 3/4 3/4 0 b-> c 0 -.278 .278 c-> d 1.027 1.027 0 d-> a -ln(2) 0 ln(2)
300
The piston is now RAPIDLY moved from x = L/2 to x = L/4. During this process, is the work done by the *diatomic* gas positive, negative, or zero?
Negative
400
Just as you are beginning to feel comfortable, a polar bear pokes a hole into the wall, causing air to leak out. Approximately how many moles of air escape from the tent if there are approximately 500 mols of air whose temperature starts and remains at 27C and the gauge pressure inside your tent is 0.2 atm?
83 mols
400
The piston is now RAPIDLY moved from x = L/2 to x = L/4. During this process, is the work done by the monatomic gas positive, negative, or zero?
positive
500
The piston is now RAPIDLY moved from x = L/2 to x = L/4. During this process, is the work done by the system of both gasses positive, negative, or zero?
Zero
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