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Consider a system of N atoms of an ideal gas of type A at temperature T and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas of type B at the same temperature T and volume V. Once the combined system reaches equilibrium.
Select one:
Select one:
- a)entropy of final system is equal to the sum of individual entropies
- b)the entropy of mixing is non-zero when the atoms A and B are of the same type
- c)the entropy of mixing is 2NKB ln 2
- d)the total entropy of final system is less than the sum of the initial entropies of the two gases
Correct answer is option 'C'. Can you explain this answer?
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Consider a system of N atoms of an ideal gas of type A at temperature ...
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Consider a system of N atoms of an ideal gas of type A at temperature ...
Entropy of Mixing in a System of Ideal Gases
Entropy is a measure of the disorder or randomness in a system. In the context of a mixture of ideal gases, the entropy of mixing refers to the increase in disorder when two different types of gas are allowed to mix together. Let's analyze the given options to determine the correct answer.
a) The entropy of mixing is 2NKB ln 2
This option suggests that the entropy of mixing is a constant value of 2NKB ln 2, where N is the number of atoms and KB is the Boltzmann constant. However, the entropy of mixing depends on the specific conditions of the system and is not a constant value. Therefore, option a) is incorrect.
b) The entropy of mixing is non-zero when the atoms A and B are of the same type
This option implies that the entropy of mixing is only non-zero when the atoms A and B are identical. However, in reality, the entropy of mixing is non-zero regardless of whether the atoms are of the same type or not. The mixing of two different types of gases always introduces disorder and increases the entropy of the system. Hence, option b) is incorrect.
c) Entropy of the final system is equal to the sum of individual entropies
This option states that the entropy of the final system is equal to the sum of the individual entropies of the two gases. This is the correct explanation of the entropy of mixing. When the two gases mix, the total number of microstates (possible arrangements of particles) increases, leading to an increase in the overall entropy. The entropy change due to mixing is given by the formula ΔS_mix = NKB ln(W_mix/W_AW_B), where W_mix is the number of microstates of the mixed system, and W_A and W_B are the number of microstates of the individual gases. As the number of particles is the same for both gases and they are at the same temperature, W_A and W_B are equal, resulting in ΔS_mix = NKB ln(2). Therefore, the entropy of the final system is equal to the sum of the individual entropies. Hence, option c) is correct.
d) The total entropy of the final system is less than the sum of the initial entropies of the two gases
This option suggests that the total entropy of the final system is less than the sum of the initial entropies of the two gases. However, this contradicts the second law of thermodynamics, which states that the entropy of an isolated system always increases or remains constant. Therefore, option d) is incorrect.
In conclusion, the correct option is c) the entropy of the final system is equal to the sum of the individual entropies.
Entropy is a measure of the disorder or randomness in a system. In the context of a mixture of ideal gases, the entropy of mixing refers to the increase in disorder when two different types of gas are allowed to mix together. Let's analyze the given options to determine the correct answer.
a) The entropy of mixing is 2NKB ln 2
This option suggests that the entropy of mixing is a constant value of 2NKB ln 2, where N is the number of atoms and KB is the Boltzmann constant. However, the entropy of mixing depends on the specific conditions of the system and is not a constant value. Therefore, option a) is incorrect.
b) The entropy of mixing is non-zero when the atoms A and B are of the same type
This option implies that the entropy of mixing is only non-zero when the atoms A and B are identical. However, in reality, the entropy of mixing is non-zero regardless of whether the atoms are of the same type or not. The mixing of two different types of gases always introduces disorder and increases the entropy of the system. Hence, option b) is incorrect.
c) Entropy of the final system is equal to the sum of individual entropies
This option states that the entropy of the final system is equal to the sum of the individual entropies of the two gases. This is the correct explanation of the entropy of mixing. When the two gases mix, the total number of microstates (possible arrangements of particles) increases, leading to an increase in the overall entropy. The entropy change due to mixing is given by the formula ΔS_mix = NKB ln(W_mix/W_AW_B), where W_mix is the number of microstates of the mixed system, and W_A and W_B are the number of microstates of the individual gases. As the number of particles is the same for both gases and they are at the same temperature, W_A and W_B are equal, resulting in ΔS_mix = NKB ln(2). Therefore, the entropy of the final system is equal to the sum of the individual entropies. Hence, option c) is correct.
d) The total entropy of the final system is less than the sum of the initial entropies of the two gases
This option suggests that the total entropy of the final system is less than the sum of the initial entropies of the two gases. However, this contradicts the second law of thermodynamics, which states that the entropy of an isolated system always increases or remains constant. Therefore, option d) is incorrect.
In conclusion, the correct option is c) the entropy of the final system is equal to the sum of the individual entropies.
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Consider a system of N atoms of an ideal gas of type A at temperature T and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas of type B at the same temperature T and volume V. Once the combined system reaches equilibrium.Select one:a)entropy of final system is equal to the sum of individual entropiesb)the entropy of mixing is non-zero when the atoms A and B are of the same typec)the entropy of mixing is 2NKB ln 2d)the total entropy of final system is less than the sum of the initial entropies of the two gasesCorrect answer is option 'C'. Can you explain this answer?
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Consider a system of N atoms of an ideal gas of type A at temperature T and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas of type B at the same temperature T and volume V. Once the combined system reaches equilibrium.Select one:a)entropy of final system is equal to the sum of individual entropiesb)the entropy of mixing is non-zero when the atoms A and B are of the same typec)the entropy of mixing is 2NKB ln 2d)the total entropy of final system is less than the sum of the initial entropies of the two gasesCorrect answer is option 'C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider a system of N atoms of an ideal gas of type A at temperature T and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas of type B at the same temperature T and volume V. Once the combined system reaches equilibrium.Select one:a)entropy of final system is equal to the sum of individual entropiesb)the entropy of mixing is non-zero when the atoms A and B are of the same typec)the entropy of mixing is 2NKB ln 2d)the total entropy of final system is less than the sum of the initial entropies of the two gasesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a system of N atoms of an ideal gas of type A at temperature T and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas of type B at the same temperature T and volume V. Once the combined system reaches equilibrium.Select one:a)entropy of final system is equal to the sum of individual entropiesb)the entropy of mixing is non-zero when the atoms A and B are of the same typec)the entropy of mixing is 2NKB ln 2d)the total entropy of final system is less than the sum of the initial entropies of the two gasesCorrect answer is option 'C'. Can you explain this answer?.
Consider a system of N atoms of an ideal gas of type A at temperature T and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas of type B at the same temperature T and volume V. Once the combined system reaches equilibrium.Select one:a)entropy of final system is equal to the sum of individual entropiesb)the entropy of mixing is non-zero when the atoms A and B are of the same typec)the entropy of mixing is 2NKB ln 2d)the total entropy of final system is less than the sum of the initial entropies of the two gasesCorrect answer is option 'C'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Consider a system of N atoms of an ideal gas of type A at temperature T and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas of type B at the same temperature T and volume V. Once the combined system reaches equilibrium.Select one:a)entropy of final system is equal to the sum of individual entropiesb)the entropy of mixing is non-zero when the atoms A and B are of the same typec)the entropy of mixing is 2NKB ln 2d)the total entropy of final system is less than the sum of the initial entropies of the two gasesCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a system of N atoms of an ideal gas of type A at temperature T and volume V. It is kept in diffusive contact with another system of N atoms of another ideal gas of type B at the same temperature T and volume V. Once the combined system reaches equilibrium.Select one:a)entropy of final system is equal to the sum of individual entropiesb)the entropy of mixing is non-zero when the atoms A and B are of the same typec)the entropy of mixing is 2NKB ln 2d)the total entropy of final system is less than the sum of the initial entropies of the two gasesCorrect answer is option 'C'. Can you explain this answer?.
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