Home
Class 11
PHYSICS
A spherical body of radius 'b' has a con...

A spherical body of radius 'b' has a concentric cavity of radius 'a' as shown. Thermal conductivity of the material is K. Find thermal resistance between inner surface P and outer surface Q.

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
As we move from P to Q surface perpendicular to PQ is spherical and its size keeps on increasing (just like different layers of a spherical onion). So, first we will calculate thermal
resistance of one layer at a distance r from centre and thickness dr by using the formula
`R = l/(KA)`

In this formula, dimension of the layer along PQ is dr and the surface area perpendicular to PQ
is `4pir^2`
`:. dR = (dr)/(K(4pir^2))`
Now, if we integrate dR from r = a to r= b, we will get the total thermal resistance between P
and Q. Thus,
` R = int_(a)^b dR = int_(a)^b (dr)/(K(4pir^2))`
Solving this expression, we get
`R = 1/(4piK)(1/a -1/b)`.
Promotional Banner

Topper's Solved these Questions

  • CALORIMETRY & HEAT TRANSFER

    DC PANDEY|Exercise Example Type 2|2 Videos

  • CALORIMETRY & HEAT TRANSFER

    DC PANDEY|Exercise Example Type 3|1 Videos

  • CALORIMETRY & HEAT TRANSFER

    DC PANDEY|Exercise Level 2 Subjective|14 Videos

  • BASIC MATHEMATICS

    DC PANDEY|Exercise Exercise|13 Videos

  • CALORIMETRY AND HEAT TRANSFER

    DC PANDEY|Exercise Medical entrance s gallery|38 Videos

Similar Questions

Explore conceptually related problems

Thermal conductivity of the conductor shown in figure is K. Find thermal resistance between points a and b. .

A metallic sphere having inner and outer radii a and b respectively has thermal conductivity K=(K_(0))/r (alerleb) Find the thermal resistance between inner surface and outer surface.

A solid spherical conductor of radius R has a spherical cavity of radius at its centre. A charge is kept at the centre of the cavity. The charge at the inner surface, outer surface are respectively.

A solid spherical conductor of radius R has a spherical cavity of radius a(a

Space between tow concentric spheres of radii r_(1) and r_(2) such that r_(1) lt r_(2) is filled with a material of resistivity rho . Find the resistance between inner and outer surface of the material

What is the volume of the material in a spherical shell with inner radius ‘r' and outer radius 'R' ?

A point source of heat of power P is placed at the centre of a spherical shell of mean radius R. The material of the shell has thermal conductivity K. If the temperature difference between the outer and inner surface of the shell in not to exceed T, the thickness of the shell should not be less than .......

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and oputer radius 2R. The thermal conductivity of the material of the inner cylinder si k_(1) and that of the outer cylinder is K_(2) ,Assumming no loss of heat , the effective thermal conductivity of the system for heat flowing along the length of the cylionder is :

Sphere of inner radius a and outer radius b is made of p uniform resistivity find resistance between inner and outer surface

A point source of heat of power P is placed at the centre of a thin spherical shell of a mean radius R. The material of the shell has thermal conductivity K. Calculate the thickness of the shell if the temperature difference between the outer and inner surfaces of the shell in steady - state is T.