EASY
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The following figure shows three different arrangements of materials 1,2, and 3 to form a wall. Thermal conductivities are k1>k2>k3. The left side of the wall is 20°C higher than the right side. Temperature difference T across the material 1 has following relation in three cases

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Important Questions on Thermal Properties of Matter

HARD
In steady state heat conduction, the equations that determine the heat current jr [heat flowing per unit time per unit area] and temperature Tr in space are exactly the same as those governing the electric field Er and electrostatic potential Vr with the equivalence given in the table below.
Heat flow Electrostatics
Tr Vr
jr Er
We exploit this equivalence to predict the rate Q of total heat flowing by conduction from the surfaces of spheres of varying radii, all maintained at the same temperature. If QRn, where R is the radius, then the value of n is
EASY
A heat source at T=103 K is connected to another heat reservoir at T=102 K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is 0.1 W K-1 m-1, the energy flux through it in the steady-state is:
MEDIUM

Three rods of same dimensions have thermal conductivities 3K, 2K and K. They are arranged as shown in the figure below. Then in the steady state the temperature of the junction 'P' is

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MEDIUM

A rod CD of thermal resistance 10 K W-1 is joined at the middle of an identical rod AB as shown in figure. The ends A, B and D are maintained at 200°C, 100°C and 125°C respectively. The heat current in CD is P W. The value of P is

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MEDIUM
A uniform copper rod of 50 cm length is insulated on the sides and has its ends exposed to ice and steam respectively. If there is a layer of water 1 mm thick at each end, the temperature gradient in °C m-1 in the bar is (assume that the thermal conductivity of copper is  400 W m-1 K-1 and water is 0.4 W m-1 K-1 )
EASY
Three rods of identical cross-sectional area and made from the same metal, form the sides of an isosceles triangle ABC right angled at B as shown in figure. The point A and B are maintained at temperature T and 2T respectively, in the steady state. Now, assuming that only heat conduction takes place. The temperature of point C will be
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EASY
Which of the following is NOT a reversible process?
MEDIUM
Two materials having coefficients of thermal conductivity 3K and K and thickness d and 3d respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are θ2 and θ1 respectively, θ2>θ1. The temperature at the interface is
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MEDIUM

Three rods of identical cross-section and length are made of three different materials of thermal conductivity K1, K2 and K3, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100°C and the other at 0°C (see figure). If the joints of the rod are at 70°C and 20°C in steady and there is no loss of energy from the surface of the rod, the correct relationship between K1, K2 and K3 is :

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MEDIUM
Two thin metallic spherical shells of radii r1 and r2r1<r2 are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature θ1 and the outer shell at temperature θ2θ1<θ2. The rate at which heat flows radially through the material is :
HARD

A thin piece of thermal conductor of constant thermal conductivity insulated on the lateral sides connects two reservoirs which are maintained at temperatures, T1 and, T2 as shown. Assuming that the system is in steady-state, which of the following plots best represents the dependence of the rate of change of entropy on the ratio of temperatures, T1T2

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MEDIUM
In a steady state, the temperature at the end A and end B of a 20 cm long rod AB are 100°C and 0°C. The temperature of a point, 9 cm from A is
EASY
Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of the combination is:
HARD
Two rods whose lengths are l1 and l2 with heat conductivity co-efficients k1 and k2 are placed end to end. The heat conductivity coefficient of a uniform rod of length l1+l2 whose conductivity is same as that of the system of these two rods is
EASY
Cloudy nights are usually warmer than clear ones, because clouds 
EASY

A piece of metal and a piece of wood are kept at a temperature of 45 °C.

On touching the two with hand,

HARD

Consider a pair of insulating blocks with thermal resistances R1, and R2 as shown in the figure. The temperature θ at the boundary between the two blocks is

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EASY
The two ends of a metal rod are maintained at temperatures 100 °C and 110 °C . The rate of heat flow in the rod is found to be 4.0 J s-1 . If the ends are maintained at temperatures 200 °C and 210 °C , the rate of heat flow will be:
MEDIUM
Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures T1=300 K and T2=100 K as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are K1 and K2, respectively. If the temperature at the junction of the two cylinders in the steady state is 200 K, then K1/K2 is

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