Home
Class 12
PHYSICS
A long rod has one end at 0^@C and other...

A long rod has one end at `0^@C` and other end at a high temperature. The coefficient of thermal conductivity varies with distance from the low temperature end as `K = K_0(1+ax)`, where `K_0 = 10^2` SI unit and `a = 1m^-1` . At what distance from the first end the temperature will be `100^@C`? The area of cross-section is `1cm^2` and rate of heat conduction is 1 W.

Text Solution

Verified by Experts

The correct Answer is:
1.71 m
Promotional Banner

Topper's Solved these Questions

  • THERMAL PROPERTIES OF MATTER

    AAKASH INSTITUTE|Exercise Assignment (Section-J) Akash Challengers Questions|7 Videos

  • THERMAL PROPERTIES OF MATTER

    AAKASH INSTITUTE|Exercise Assignment (Section-H) Multiple True-False Type Questions|2 Videos

  • TEST 9

    AAKASH INSTITUTE|Exercise EXAMPLE|61 Videos

  • THERMODYNAMICS

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION -D) (Assertion - Reason Type Questions)|10 Videos

Similar Questions

Explore conceptually related problems

A rod of length l with thermally insulated lateral surface is made of a material whose thermal conductivity varies as K=sc//T where c is a constant. The ends are kept at temperatures T_(1) and T_(2) . Find the temperature at a distance x from te first end where the temperature is T_(1) and the heat flow density.

A rod of length l with thermally insulated lateral surface is made of a matrical whose thermal conductivity varies as K =C//T where C is a constant The ends are kept at temperature T_(1) and T_(2) The temperature at a distance x from the first end where the temperature is T_(1), T =T_(1)((T_(2))/(T_(1)))^(nx//2l) Find the value of n? .

A rod AB is 1m long. The temperature of its one end A is maintained at 100^(@) C and other end B at 10^(@) C, the temperature at a distance of 60 cm from point B is

A rod of length l (laterally thermally insulated) of the uniform cross sectional area A consists of a material whose thermal conductivity varies with temperature as K=(K_(0))/(a+bT') where K_(0) , a and b are constants. T_(1) and T_(2)(lt T_(1)) are the temperatures of the ends of the rod. Then, the rate of flow of heat across the rod is

A rod of length l with thermally insulated lateral surface consists of material whose heat conductivity coefficient varies with temperature as k= a//T , where a is a constant. The ends of the rod are kept at temperatures T_1 and T_2 . Find the function T(x), where x is the distance from the end whose temperature is T_1 .

Heat is flowing through a rod of length 25.0 cm having cross-sectional area 8.80 cm^(2) . The coefficient of thermal conductivity for the material of the rod is K = 9.2 xx 10^(-2) kcal s^(-1) m^(-1) .^(@)C^(-1) . The Temperatures of the ends of the rod are 125^(@)C and 0^(@)C in the steady state. Calculate (i) temeprature gradient in the rod (ii) temperature of a point at a distance of 10.0 cm from the hot end and (iii) rate of flow of heat.

The end A of rod AB of length 1 m is maintained at 80^(@) C and the end B at 0^(@) C. The temperature at a distance of 60 cm from the end A is

A rod of length L with sides fully insulated is made of a material whose thermal conductivity K varies with temperature as K=(alpha)/(T) where alpha is constant. The ends of rod are at temperature T_(1) and T_(2)(T_(2)gtT_(1)) Find the rate of heat flow per unit area of rod .

The ends of a cylinder steel rod are maintained at two different temperatures. The rod conducts heat from one end to the other at a rate of 10 cal // s. At what rate would a steel rod twice as long and twice the diameter conduct heat between the same two temperatures?

Two identical rods AB and CD, each of length L are connected as shown in figure-4.22. Their cross-sectional area is A and their thermal conductivity is k. Ends A, C and D are maintained at temperatures T_(1),T_(2) and T_(3) respectively. Neglecting heat loss to the surroundings, find the temperature at B.