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Chapter 15: Problem 46

List these in order of increasing entropy: (a) 0.01 mol of \(\mathrm{N}_{2}\) gas in a \(1-\mathrm{L}\) container at \(0^{\circ} \mathrm{C} ;\) (b) 0.01 mol of \(\mathrm{N}_{2}\) gas in a 2 -L container at \(0^{\circ} \mathrm{C} ;\) (c) 0.01 mol of liquid \(\mathrm{N}_{2}\).

Short Answer

Expert verified
Question: Arrange the following conditions in order of increasing entropy: (a) nitrogen gas in a 1-L container, (b) nitrogen gas in a 2-L container, and (c) liquid nitrogen in a 1-L container. Answer: The order of increasing entropy is (c) < (a) < (b).

Step by step solution

01

Compare the physical state of the substance

In this exercise, we have two cases with nitrogen gas and one case with liquid nitrogen. As a general rule, gases have higher entropy than liquids because the particles in gases have greater freedom of motion and are more randomly distributed than in liquids. So, the order of entropy based on the state of the substance would be (c) < (a) or (b)
02

Compare the size of the container

Next, let's consider the size of the container. We have two cases with nitrogen gas: one in 1-L container (a) and another in a 2-L container (b). Since larger volumes provide more room for the gas particles to move around and create more disorder, we can conclude that the entropy of the system increases when the volume of the container increases. So, the order of entropy based on the volume of the container is (a) < (b).
03

Combine the factors

Now, let's put together the findings from step 1 and step 2. Comparing the cases considering the differences in physical state and volume, we arrive at the final order of increasing entropy: (c) < (a) < (b).

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Most popular questions from this chapter

An air conditioner whose coefficient of performance is 2.00 removes $1.73 \times 10^{8} \mathrm{J}$ of heat from a room per day. How much does it cost to run the air conditioning unit per day if electricity costs \(\$ 0.10\) per kilowatt-hour? (Note that 1 kilowatt-hour \(=3.6 \times 10^{6} \mathrm{J} .\) )
A town is considering using its lake as a source of power. The average temperature difference from the top to the bottom is \(15^{\circ} \mathrm{C},\) and the average surface temperature is \(22^{\circ} \mathrm{C} .\) (a) Assuming that the town can set up a reversible engine using the surface and bottom of the lake as heat reservoirs, what would be its efficiency? (b) If the town needs about \(1.0 \times 10^{8} \mathrm{W}\) of power to be supplied by the lake, how many \(\mathrm{m}^{3}\) of water does the heat engine use per second? (c) The surface area of the lake is $8.0 \times 10^{7} \mathrm{m}^{2}$ and the average incident intensity (over \(24 \mathrm{h})\) of the sunlight is \(200 \mathrm{W} / \mathrm{m}^{2} .\) Can the lake supply enough heat to meet the town's energy needs with this method?
An inventor proposes a heat engine to propel a ship, using the temperature difference between the water at the surface and the water \(10 \mathrm{m}\) below the surface as the two reservoirs. If these temperatures are \(15.0^{\circ} \mathrm{C}\) and \(10.0^{\circ} \mathrm{C},\) respectively, what is the maximum possible efficiency of the engine?
If the pressure on a fish increases from 1.1 to 1.2 atm, its swim bladder decreases in volume from \(8.16 \mathrm{mL}\) to \(7.48 \mathrm{mL}\) while the temperature of the air inside remains constant. How much work is done on the air in the bladder?
For a more realistic estimate of the maximum coefficient of performance of a heat pump, assume that a heat pump takes in heat from outdoors at $10^{\circ} \mathrm{C}$ below the ambient outdoor temperature, to account for the temperature difference across its heat exchanger. Similarly, assume that the output must be \(10^{\circ} \mathrm{C}\) hotter than the house (which itself might be kept at \(20^{\circ} \mathrm{C}\) ) to make the heat flow into the house. Make a graph of the coefficient of performance of a reversible heat pump under these conditions as a function of outdoor temperature (from $\left.-15^{\circ} \mathrm{C} \text { to }+15^{\circ} \mathrm{C} \text { in } 5^{\circ} \mathrm{C} \text { increments }\right)$
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