Tag: the second law of thermodynamics

Questions Related to the second law of thermodynamics

State whether true or false :

Water cannot be converted into ice by adding ice to it.

physics heat engine: second law of thermodynamics second law of thermodynamics the second law of thermodynamics second law of thermodynamic

  1. True

  2. False

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Correct Option: B
Explanation:

The given statement is false.

Here, both ice and water are at same temperature so that water cannot give out Latent heat to the ice and hence it does not freeze.

Which is not true for Second Law of Thermodynamics?

physics heat engine: second law of thermodynamics second law of thermodynamics the second law of thermodynamics second law of thermodynamic

  1. The second law of thermodynamics states that the total entropy of an isolated system always increases over time, or remains constant in ideal cases where the system is in a steady state or undergoing a reversible process.

  2. It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.

  3. It is impossible to construct an engine which will work in a complete cycle, and produce no effect except the raising of a weight and cooling of a heat reservoir.

  4. The second law of thermodynamics states that the total energy of an isolated system is constant.

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Correct Option: D
Explanation:
The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. The total entropy can remain constant in ideal cases where the system is in a steady state (equilibrium), or is undergoing a reversible process. In all spontaneous processes, the total entropy always increases and the process is irreversible. The increase in entropy accounts for the irreversibility of natural processes, and the asymmetry between future and past.

Historically, the second law was an empirical finding that was accepted as an axiom of thermodynamic theory. Statistical mechanics, classical or quantum, explains the microscopic origin of the law.
Hence option D is only incorrect option.

During the phase change, when water freezes, its converted to ice in which molecules is in more structured order. Why doesn't this contradict the Second Law of Thermodynamics?

physics heat engine: second law of thermodynamics second law of thermodynamics the second law of thermodynamics second law of thermodynamic

  1. Because the density of the water is decreasing

  2. Because the water is gaining entropy as it goes from liquid to solid state

  3. Because the water's internal energy is decreasing

  4. Because the surroundings are losing entropy

  5. Because the surroundings are gaining entropy

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Correct Option: E
Explanation:

The heat energy released during the freezing of water goes to the surrounding which increases the entropy of the surrounding. Thus although the entropy of the water decreases, the entropy of the surrounding increases such that the net entropy of system (water) and surrounding is greater than zero which does not violate the Second Law.

Hence option E is correct.

An inventor claims to have developed an engine that takes in $1000\  J$ of heat and produces $1500\  J$ of work during each cycle. Comment on the validity of this claim.

physics heat engine: second law of thermodynamics second law of thermodynamics the second law of thermodynamics second law of thermodynamic

  1. The proposed engine claims to produce more work in a cyclic process than the amount of heat that is supplied, so it is in violation of the first law of thermodynamics.

  2. The statement is completely valid as it increases the efficiency by increasing the work output.

  3. The proposed engine claims to produce more work in a cyclic process than the amount of heat that is supplied, so it is in violation of the zeroth law of thermodynamics.

  4. None of these

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Correct Option: A
Explanation:

An inventor claims to have developed an engine that takes in 1000 J of heat and produces 1500 J of work during each cycle.The proposed engine claims to produce more work in a cyclic process than the amount of heat that is supplied, so it is in violation of the first law of thermodynamics.

The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems. The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed. The first law is often formulated.
${\displaystyle \Delta U=Q-W.}$

Calculate the least amount of work that must be done to freeze one gram of water at $0^0C$ by means of the refrigerator.The temperature of the surrounding is $27^0C$.How much heat is passed on the surrounding in this process? Latent heat of fusion $L=80\ cal/g$.

physics heat engine: second law of thermodynamics second law of thermodynamics the second law of thermodynamics second law of thermodynamic

  1. $87.91\ cal$

  2. $97.91\ cal$

  3. $88.95\ cal$

  4. $89.95\ cal$

Show answer
Correct Option: A
Explanation:

$L=80 \dfrac{cal}{g}$

$m=1g$
$T _1=27°=300K$
$T _2=0°=273K$
Least work done $W=L \times m \times \dfrac{T _1}{T _2}$
=$80 \times 1 \times \dfrac{300}{273}$
=$87.912 cal$

A heat engine takes in $700\  J$ of heat from high-temperaturere reservoir and rejects $500\  J$ of heat to a lower temperature reservoir. How much work does the engine do in each cycle?

physics heat engine: second law of thermodynamics second law of thermodynamics the second law of thermodynamics second law of thermodynamic

  1. $100\ J$

  2. $20\ J$

  3. $200\ J$

  4. $10\ J$

Show answer
Correct Option: C
Explanation:

Given, $Q _h=700 J$ and $Q _c=500 J$

The work done by a heat engine is given by $W=Q _h=Q _c=700-500=200 J$

Calculate the efficiency of a Carnot engine operating between temperatures of 900 K and 300 K.

physics heat engine: second law of thermodynamics second law of thermodynamics the second law of thermodynamics second law of thermodynamic

  1. $87$ %

  2. $67$ %

  3. $100$ %

  4. $45$ %

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Correct Option: B
Explanation:

Given, the temperature of hot reservoir, $T _h=900 K$ and temperature of cold reservoir, $T _c=300 K$

Thus, the efficiency of the Carnot engine is $\eta=(1-T _c/T _h)\times 100=(1-300/900)\times 100=66.67 $ % $\sim 67$ % 

Heat is supplied to a diatomic gas at constant pressure. The ratio of $\Delta Q:$$\Delta$U:$\Delta$W is:

physics heat engine: second law of thermodynamics second law of thermodynamics the second law of thermodynamics second law of thermodynamic

  1. 5:3:2

  2. 7:5:2

  3. 2:3:5

  4. 2:5:7

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Correct Option: B
Explanation:
For a diatomic gas,

$C _V=\dfrac 52R$

$C _P=\dfrac 72 R$

We know that
$\therefore \Delta Q=nC _P \Delta T=n (\dfrac 72 R)\Delta T$

$\Delta U=nC _V \Delta T=n(\dfrac 52 R)\Delta T$

According to first law of thermodynamics,

$\Delta W=\Delta Q-\Delta U=nR \Delta T$

$\therefore \Delta Q: \Delta U: \Delta W=7:5:2$

What would be the efficiency of a Carnot engine operating with boiling water as one reservoir and a freezing mixture of ice and water as the other reservoir?

physics heat engine: second law of thermodynamics second law of thermodynamics the second law of thermodynamics second law of thermodynamic

  1. $27$ %

  2. $77$ %

  3. $20$ %

  4. $67$ %

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Correct Option: A
Explanation:

The boiling point of water is $100 ^oC$ and freezing point of water is $0^o C$

Thus, $T _h=100+273=373 K$ and $T _c=0+273=273 K$
The efficiency of a Carnot engine , $\eta=(1-\dfrac{T _c}{T _h})\times 100=[1-{373}/{273}]\times 100=26.8\sim 27$ %

Which of the following is not a path function ?

physics heat engine: second law of thermodynamics second law of thermodynamics the second law of thermodynamics second law of thermodynamic

  1. $\Delta$ Q

  2. $\Delta$ Q + $\Delta$ W

  3. $\Delta$ W

  4. $\Delta$ Q - $\Delta$ W

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Correct Option: D
Explanation:

$\Delta Q=\Delta U+\Delta W\ \Delta Q-\Delta W=\Delta U$

$\Delta U$ is internal energy which is independent of path.