Concepts Of Physics MCQ Edition [Volume 2]
- Exam
- Concepts Of Physics MCQ Edition [Volume 2]
- Subject
- Physics
- Chapter
- Heat Transfer
Concepts Of Physics MCQ Edition [Volume 2] · Physics · Heat Transfer
A hollow metallic sphere of radius 20 cm encloses a concentric...
A hollow metallic sphere of radius encloses a concentric metallic sphere of radius . The region between the two spheres is filled with a nonmetallic material. The inner and outer spheres are maintained at temperatures of 50^{}^{{}^{\circ}} \text{C} and 10^{}^{{}^{\circ}} \text{C} respectively, and it is observed that of heat travels from the inner sphere to the outer sphere per second. Determine the thermal conductivity of the material between the spheres.
Options
- A\dfrac{150}{\pi} \text{ W m}^{-1}^{}^{{}^{\circ}}\textC^{-1}
- B\dfrac{25}{8\pi} \text{ W m}^{-1}^{}^{{}^{\circ}}\textC^{-1}
- C\dfrac{75}{4\pi} \text{ W m}^{-1}^{}^{{}^{\circ}}\textC^{-1}
- D\dfrac{75}{8\pi} \text{ W m}^{-1}^{}^{{}^{\circ}}\textC^{-1}
Correct answer
D. \dfrac{75}{8\pi} \text{ W m}^{-1}^{}^{{}^{\circ}}\textC^{-1}
Step-by-step solution
The rate of heat flow through a spherical shell of inner radius and outer radius is given by
where is the thermal conductivity of the material.
Given:
T_1 = 50^{}^{{}^{\circ}} \text{C}
T_2 = 10^{}^{{}^{\circ}} \text{C}
Substituting the values into the formula:
K = \dfrac{15}{1.6 \pi} = \dfrac{150}{16 \pi} = \dfrac{75}{8 \pi} \text{ W m}^{-1}^{}^{{}^{\circ}}\textC^{-1}
where is the thermal conductivity of the material.
Given:
T_1 = 50^{}^{{}^{\circ}} \text{C}
T_2 = 10^{}^{{}^{\circ}} \text{C}
Substituting the values into the formula:
K = \dfrac{15}{1.6 \pi} = \dfrac{150}{16 \pi} = \dfrac{75}{8 \pi} \text{ W m}^{-1}^{}^{{}^{\circ}}\textC^{-1}