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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

From Table \(14.4,\) we know that approximately \(2256 \mathrm{kJ}\) are needed to transform \(1.00 \mathrm{kg}\) of water at \(100^{\circ} \mathrm{C}\) to steam at \(100^{\circ} \mathrm{C}\). What is the change in entropy of \(1.00 \mathrm{kg}\) of water evaporating at \(100.0^{\circ} \mathrm{C} ?\) (Specify whether the change in entropy is an increase, \(+\), or a decrease, \(-.\) )
(a) How much heat does an engine with an efficiency of \(33.3 \%\) absorb in order to deliver \(1.00 \mathrm{kJ}\) of work? (b) How much heat is exhausted by the engine?
Two engines operate between the same two temperatures of \(750 \mathrm{K}\) and \(350 \mathrm{K},\) and have the same rate of heat input. One of the engines is a reversible engine with a power output of \(2.3 \times 10^{4} \mathrm{W} .\) The second engine has an efficiency of \(42 \% .\) What is the power output of the second engine?
(a) What is the entropy change of 1.00 mol of \(\mathrm{H}_{2} \mathrm{O}\) when it changes from ice to water at \(0.0^{\circ} \mathrm{C} ?\) (b) If the ice is in contact with an environment at a temperature of \(10.0^{\circ} \mathrm{C}\) what is the entropy change of the universe when the ice melts?
Suppose you mix 4.0 mol of a monatomic gas at \(20.0^{\circ} \mathrm{C}\) and 3.0 mol of another monatomic gas at \(30.0^{\circ} \mathrm{C} .\) If the mixture is allowed to reach equilibrium, what is the final temperature of the mixture? [Hint: Use energy conservation.]
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