Question 1

A 4.00-liter container is divided into two equal parts,one part containing 0.0100 mole of neon,and the other part containing 0.0100 mole of helium.The divider is removed and the gases mix.What is the change in entropy (in J/K)of this system?

Accepted Answer

The change in entropy for mixing two ideal gases can be calculated using the formula ΔS = -nR[ xln(x) + yln(y) ], where n is the total moles of gas, R is the gas constant (8.314 J/mol·K), and x and y are the mole fractions of the two gases. Since both gases have the same amount, x = y = 0.5. The total moles n = 0.0200 moles. Plugging these values into the formula gives ΔS = 0.115 J/K.

Question 2

One end of a copper rod is in thermal contact with a hot reservoir at T = 500 K and the other end is in thermal contact with a cooler reservoir at T = 300 K.Find the entropy change of each reservoir,and the total entropy change,when 8 000 J of heat energy are conducted from one end of the rod to the other with no change in the temperature distribution in the rod.

Accepted Answer

The answer of One end of a copper rod is...

Question 3

For a gas of N identical molecules of molecular volume V_m in total volume V at temperature T,the number of ways of locating the N molecules in the volume is

Accepted Answer

The number of ways of locating the N molecules in the volume is given by:
W=N!/(n1!n2!....nk!) *(V/n)^N
where ni is the number of molecules in the i-th subvolume of V divided into N subvolumes of equal volume V/N.
Here, we have only one subvolume, so k=1, ni=N, V/n=Vs (volume per molecule),
hence W=N!/(N!VS^N)=(1/VS)^N
Now substituting VS=V/N-U1B1mS1U1B0, we get:
W=N!(N-U1B1mS1U1B0 N)N/2 .... 1/(V/N-U1B1mS1U1B0)^N
which is a number with a leading digit 5, so the correct answer is (D).

Question 4

A violation of the second law of thermodynamics would occur if

Accepted Answer

The answer of A violation of the second law of...

Question 5

Selena states that 
Proves that entropy has a definite value at the beginning and end of an adiabatic free expansion.Ron says 
,where W is the number of microstates of a given macrostate.Which one,if either,is correct?

Accepted Answer

The answer of Selena states that 
Proves that entropy has...

Question 6

In a nuclear power plant,the reactor produces 500°C steam that is used to power the steam turbines which generate 1 500 MW of electrical power.The cooling tower eliminates the waste heat at 50°C.If the efficiency of the plant were that of a Carnot engine,at what rate would waste heat be vented to the atmosphere?

Accepted Answer

The answer of In a nuclear power plant,the reactor produces...

Question 7

Every second at Niagara Falls,some 5000 m³ of water falls a distance of 50 m.What is the increase in entropy per second due to the falling water? (Assume a 20°C environment).

Accepted Answer

The answer of Every second at Niagara Falls,some 5000 m³...

Question 8

A violation of the second law of thermodynamics would occur if

Accepted Answer

The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time, and is constant if and only if all processes are reversible. It also states that heat cannot spontaneously flow from a colder location to a hotter location. Thus, a ball spontaneously starting to bounce (a) and heat moving from a cold object to a hot object (b) would violate this law. However, a refrigerator heating the air in a room is in accordance with the second law, as it moves heat from inside the refrigerator to the outside, increasing the room's temperature while being powered by an external energy source.

Question 9

For the same temperature increase in a system,the change in entropy,ΔS,is largest in a reversible

Accepted Answer

For a given temperature increase, the change in entropy (ΔS) is largest in a constant pressure process because it allows for the system to do work on its surroundings (due to volume expansion) in addition to the heat added to the system, leading to a greater overall change in entropy compared to other processes listed.

Question 10

Suppose there are 3 molecules in a container.If each molecule has a 1-in-2 chance of being in the left half of the container,what is the probability that there are exactly 2 molecules in the left half of the container?

Accepted Answer

There are a total of 2^3 = 8 possible arrangements for the molecules. We can use the binomial distribution to find the probability of exactly 2 molecules being in the left half of the container. The probability of a single molecule being in the left half is 1/2, and the probability of it being in the right half is also 1/2.
P(exactly 2 in left half) = (3 choose 2) * (1/2)^2 * (1/2)^1 = 3/8
Therefore, the answer is D).

Question 11

For a pair of dice,how many microstates are there that result in the macrostate of rolling a 7?

Accepted Answer

There are six ways to roll a 7 with two dice: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). Each roll of the dice is independent, so there is only one microstate for each of these ways to roll a 7, giving a total of 6 microstates.

Question 12

In an engine operating in the Otto cycle,the final volume of the fuel-air mixture is one sixth the initial volume.Assume γ = 1.4.The maximum theoretical efficiency of this cycle,in per cent,is

Accepted Answer

In the Otto cycle,
We know, efficiency, 
η = 1 - (1/r^(γ-1)) where r is compression ratio.
Given, final volume (V2) = 1/6(initial volume(V1))
V1/V2 = 6
r = (V1/V2)=6
η = 1 - (1/6)^(1.4-1) = 0.51 or 51%. 
Therefore, the correct choice is C.

Question 13

What is the probability of rolling either a 7 or 11 on a single roll of a pair of dice?

Accepted Answer

The answer of What is the probability of rolling either...

Question 14

Which answer below is not a statement of the second law of thermodynamics?

Accepted Answer

Choice D is a statement about reversible processes, but does not explicitly state the second law of thermodynamics. The other choices all directly relate to the second law.

Question 15

The thermal efficiency of a heat engine is given by

Accepted Answer

The answer of The thermal efficiency of a heat engine...

Quiz 22: Heat Engines, entropy, and the Second Law of Thermodynamics

A 4.00-liter container is divided into two equal parts,one part containing 0.0100 mole of neon,and the other part containing 0.0100 mole of helium.The divider is removed and the gases mix.What is the change in entropy (in J/K) of this system?

For a gas of N identical molecules of molecular volume V_m in total volume V at temperature T,the number of ways of locating the N molecules in the volume is

A violation of the second law of thermodynamics would occur if

Selena states that Proves that entropy has a definite value at the beginning and end of an adiabatic free expansion.Ron says ,where W is the number of microstates of a given macrostate.Which one,if either,is correct?

Every second at Niagara Falls,some 5000 m³ of water falls a distance of 50 m.What is the increase in entropy per second due to the falling water? (Assume a 20°C environment).

A violation of the second law of thermodynamics would occur if

For the same temperature increase in a system,the change in entropy,ΔS,is largest in a reversible

Suppose there are 3 molecules in a container.If each molecule has a 1-in-2 chance of being in the left half of the container,what is the probability that there are exactly 2 molecules in the left half of the container?

For a pair of dice,how many microstates are there that result in the macrostate of rolling a 7?

In an engine operating in the Otto cycle,the final volume of the fuel-air mixture is one sixth the initial volume.Assume γ = 1.4.The maximum theoretical efficiency of this cycle,in per cent,is

What is the probability of rolling either a 7 or 11 on a single roll of a pair of dice?

Which answer below is not a statement of the second law of thermodynamics?

The thermal efficiency of a heat engine is given by

Quiz 22: Heat Engines, entropy, and the Second Law of Thermodynamics

A 4.00-liter container is divided into two equal parts,one part containing 0.0100 mole of neon,and the other part containing 0.0100 mole of helium.The divider is removed and the gases mix.What is the change in entropy (in J/K) of this system?

For a gas of N identical molecules of molecular volume Vm in total volume V at temperature T,the number of ways of locating the N molecules in the volume is

A violation of the second law of thermodynamics would occur if

Selena states that Proves that entropy has a definite value at the beginning and end of an adiabatic free expansion.Ron says ,where W is the number of microstates of a given macrostate.Which one,if either,is correct?

Every second at Niagara Falls,some 5000 m3 of water falls a distance of 50 m.What is the increase in entropy per second due to the falling water? (Assume a 20°C environment).

A violation of the second law of thermodynamics would occur if

For the same temperature increase in a system,the change in entropy,ΔS,is largest in a reversible

Suppose there are 3 molecules in a container.If each molecule has a 1-in-2 chance of being in the left half of the container,what is the probability that there are exactly 2 molecules in the left half of the container?

For a pair of dice,how many microstates are there that result in the macrostate of rolling a 7?

In an engine operating in the Otto cycle,the final volume of the fuel-air mixture is one sixth the initial volume.Assume γ = 1.4.The maximum theoretical efficiency of this cycle,in per cent,is

What is the probability of rolling either a 7 or 11 on a single roll of a pair of dice?

Which answer below is not a statement of the second law of thermodynamics?

The thermal efficiency of a heat engine is given by

For a gas of N identical molecules of molecular volume V_m in total volume V at temperature T,the number of ways of locating the N molecules in the volume is

Every second at Niagara Falls,some 5000 m³ of water falls a distance of 50 m.What is the increase in entropy per second due to the falling water? (Assume a 20°C environment).