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Blackbody radiation at temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. What is the final temperature of the system? i) T/8 , ii) T / 2 , iii) Tln8 , iv) 2T?
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Blackbody radiation at temperature T fills a cavity of volume V. The s...
Final temperature of the system after adiabatic and reversible expansion
1. Adiabatic and reversible expansion:
In an adiabatic and reversible process, there is no heat exchange with the surroundings, and the system is in thermodynamic equilibrium throughout the process. This means that the entropy of the system remains constant.
2. Blackbody radiation:
Blackbody radiation refers to the electromagnetic radiation emitted by an idealized object called a blackbody. A blackbody absorbs all incident radiation and emits radiation at all wavelengths and frequencies. The intensity and spectrum of blackbody radiation depend on the temperature of the object.
3. Relationship between temperature and volume:
According to the Stefan-Boltzmann law, the total radiant power emitted by a blackbody is proportional to the fourth power of its absolute temperature (T). Therefore, as the temperature of the system increases, the volume of the cavity also increases.
4. Expansion of the system:
Given that the system expands adiabatically and reversibly to a final volume of 8V, we can conclude that the temperature of the system will also change.
5. Final temperature of the system:
Since the total radiant power emitted by a blackbody is proportional to the fourth power of its absolute temperature, we can write the following relationship:
(T1)^4 * V1 = (T2)^4 * V2
Where T1 is the initial temperature, V1 is the initial volume, T2 is the final temperature, and V2 is the final volume.
In this case, the initial volume is V and the final volume is 8V. Therefore, the equation becomes:
(T1)^4 * V = (T2)^4 * (8V)
Simplifying the equation, we have:
(T1)^4 = 8^4 * (T2)^4
Taking the fourth root of both sides, we get:
T1 = 8 * T2
Therefore, the final temperature of the system (T2) is T1/8.
Answer: i) T/8
1. Adiabatic and reversible expansion:
In an adiabatic and reversible process, there is no heat exchange with the surroundings, and the system is in thermodynamic equilibrium throughout the process. This means that the entropy of the system remains constant.
2. Blackbody radiation:
Blackbody radiation refers to the electromagnetic radiation emitted by an idealized object called a blackbody. A blackbody absorbs all incident radiation and emits radiation at all wavelengths and frequencies. The intensity and spectrum of blackbody radiation depend on the temperature of the object.
3. Relationship between temperature and volume:
According to the Stefan-Boltzmann law, the total radiant power emitted by a blackbody is proportional to the fourth power of its absolute temperature (T). Therefore, as the temperature of the system increases, the volume of the cavity also increases.
4. Expansion of the system:
Given that the system expands adiabatically and reversibly to a final volume of 8V, we can conclude that the temperature of the system will also change.
5. Final temperature of the system:
Since the total radiant power emitted by a blackbody is proportional to the fourth power of its absolute temperature, we can write the following relationship:
(T1)^4 * V1 = (T2)^4 * V2
Where T1 is the initial temperature, V1 is the initial volume, T2 is the final temperature, and V2 is the final volume.
In this case, the initial volume is V and the final volume is 8V. Therefore, the equation becomes:
(T1)^4 * V = (T2)^4 * (8V)
Simplifying the equation, we have:
(T1)^4 = 8^4 * (T2)^4
Taking the fourth root of both sides, we get:
T1 = 8 * T2
Therefore, the final temperature of the system (T2) is T1/8.
Answer: i) T/8
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Blackbody radiation at temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. What is the final temperature of the system? i) T/8 , ii) T / 2 , iii) Tln8 , iv) 2T?
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Blackbody radiation at temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. What is the final temperature of the system? i) T/8 , ii) T / 2 , iii) Tln8 , iv) 2T? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Blackbody radiation at temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. What is the final temperature of the system? i) T/8 , ii) T / 2 , iii) Tln8 , iv) 2T? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Blackbody radiation at temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. What is the final temperature of the system? i) T/8 , ii) T / 2 , iii) Tln8 , iv) 2T?.
Blackbody radiation at temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. What is the final temperature of the system? i) T/8 , ii) T / 2 , iii) Tln8 , iv) 2T? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Blackbody radiation at temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. What is the final temperature of the system? i) T/8 , ii) T / 2 , iii) Tln8 , iv) 2T? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Blackbody radiation at temperature T fills a cavity of volume V. The system expands adiabatically and reversibly to a volume equal to 8V. What is the final temperature of the system? i) T/8 , ii) T / 2 , iii) Tln8 , iv) 2T?.
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