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A cylinder of radius R made of a material of th er mal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is
  • a)
    K1 + K2
  • b)
    K1K2 / (K1 + K2)
  • c)
    (K1 + 3K2) / 4
  • d)
    (3K1 + 3K2) / 4
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A cylinder of radius R made of a material of th er mal conductivity K1...
Total transfer of heat per second through the composite = Heat transfer per second from material with thermal conductivity K1 + Heat transfer per second from material with thermal conductivity K2.
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A cylinder of radius R made of a material of th er mal conductivity K1...
Explanation:

  • The system consists of a cylinder of radius R made of a material of thermal conductivity K1 surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K2.

  • The two ends of the combined system are maintained at two different temperatures.

  • There is no loss of heat across the cylindrical surface and the system is in steady state.

  • To find the effective thermal conductivity of the system, we can use the concept of thermal resistance.

  • The thermal resistance of the cylinder of radius R is (ln(2R/R))/(2πK1R).

  • The thermal resistance of the cylindrical shell of inner radius R and outer radius 2R is (ln(2R/R))/(2πK2R) - (ln(2))/(2πK2R).

  • The total thermal resistance of the system is the sum of the thermal resistance of the cylinder and the thermal resistance of the cylindrical shell.

  • Therefore, the total thermal resistance of the system is (ln(2R/R))/(2πK1R) + (ln(2))/(2πK2R) - (ln(2R/R))/(2πK2R).

  • The effective thermal conductivity of the system is the reciprocal of the total thermal resistance.

  • Therefore, the effective thermal conductivity of the system is (2πK1K2R)/(2(K1 + 3K2)).

  • Simplifying the expression, we get (K1 + 3K2)/4.

  • Therefore, the correct option is (C) (K1 + 3K2)/4.

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A cylinder of radius R made of a material of th er mal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system isa)K1 + K2b)K1K2 / (K1 + K2)c)(K1 + 3K2) / 4d)(3K1 + 3K2) / 4Correct answer is option 'C'. Can you explain this answer?
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A cylinder of radius R made of a material of th er mal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system isa)K1 + K2b)K1K2 / (K1 + K2)c)(K1 + 3K2) / 4d)(3K1 + 3K2) / 4Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A cylinder of radius R made of a material of th er mal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system isa)K1 + K2b)K1K2 / (K1 + K2)c)(K1 + 3K2) / 4d)(3K1 + 3K2) / 4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cylinder of radius R made of a material of th er mal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system isa)K1 + K2b)K1K2 / (K1 + K2)c)(K1 + 3K2) / 4d)(3K1 + 3K2) / 4Correct answer is option 'C'. Can you explain this answer?.
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