418
10 Heat and Matter
of the air inside is 70 cm of Hg and the temperature 20 ◦ C. What does the
pressure become if the 100 cc bulb is kept at 20 ◦ C and the other is heated
to 100 ◦ C?
[University of Durham]
10.2.3 Heat Transfer
10.19 Two slabs of cross-sectional area A and of thickness d 1 and d 2 and thermal
conductivities k 1 and k 2 are arranged in contact face to face. The outer face
of the first slab is maintained at temperature T 1
◦ C, that of the second one at
T 2
◦ C and the interface at T ◦ C. Calculate
(a) Rate of flow of heat through the composite slab
(b) The interface temperature
(c) The equivalent conductivity
10.20 n slabs of the same thickness, the cross-sectional area A 1 , A 2 , . . . , A n and
thermal conductivities k 1 , k 2 , . . . , k n are placed in contact in parallel and
maintained at temperatures T 1 and T 2 . Calculate
(a) the rate of flow of heat through the composite slab
(b) the equivalent conductivity
10.21 A bar of copper and a bar of iron of equal length are welded together end
to end and are lagged. Determine the temperature of the interface when the
free end of the copper bar is at 100 ◦ C and the free end of the iron is at
0 ◦ C and the conditions are steady. Thermal conductivities: copper = 92,
iron = 16 cal/m/s/ ◦ C.
[University of Durham]
10.22 A block of ice is kept pressed against one end of a circular copper bar of
diameter 2 cm, length 20 cm, thermal conductivity 90 SI units and the other
end is kept at 100 ◦ C by means of a steam chamber. How long will it take
to melt 50 g of ice assuming heat is only supplied to the ice along the bar,
L = 8 × 10 4 cal/kg.
[University of Dublin]
10.23 At low temperatures, say below 50 K, the thermal conductivity of a metal
is proportional to the absolute temperature, that is, k = aT , where a is a
constant with a numerical value that depends on the particular metal. Show
that the rate of heat flow through a rod of length L and cross-sectional area A
and whose ends are at temperatures T 1 and T 2 is given by Q =
a A
2L
(T 2
1 −T 2
2 ).
10.24 Find the radial flow of heat in a material of thermal conductivity placed
between two concentric spheres of radii r 1 and r 2 (r 1 < r 2 ) which are maintained at temperatures T 1 and T 2 (T 1 > T 2 ).
10 Heat and Matter
of the air inside is 70 cm of Hg and the temperature 20 ◦ C. What does the
pressure become if the 100 cc bulb is kept at 20 ◦ C and the other is heated
to 100 ◦ C?
[University of Durham]
10.2.3 Heat Transfer
10.19 Two slabs of cross-sectional area A and of thickness d 1 and d 2 and thermal
conductivities k 1 and k 2 are arranged in contact face to face. The outer face
of the first slab is maintained at temperature T 1
◦ C, that of the second one at
T 2
◦ C and the interface at T ◦ C. Calculate
(a) Rate of flow of heat through the composite slab
(b) The interface temperature
(c) The equivalent conductivity
10.20 n slabs of the same thickness, the cross-sectional area A 1 , A 2 , . . . , A n and
thermal conductivities k 1 , k 2 , . . . , k n are placed in contact in parallel and
maintained at temperatures T 1 and T 2 . Calculate
(a) the rate of flow of heat through the composite slab
(b) the equivalent conductivity
10.21 A bar of copper and a bar of iron of equal length are welded together end
to end and are lagged. Determine the temperature of the interface when the
free end of the copper bar is at 100 ◦ C and the free end of the iron is at
0 ◦ C and the conditions are steady. Thermal conductivities: copper = 92,
iron = 16 cal/m/s/ ◦ C.
[University of Durham]
10.22 A block of ice is kept pressed against one end of a circular copper bar of
diameter 2 cm, length 20 cm, thermal conductivity 90 SI units and the other
end is kept at 100 ◦ C by means of a steam chamber. How long will it take
to melt 50 g of ice assuming heat is only supplied to the ice along the bar,
L = 8 × 10 4 cal/kg.
[University of Dublin]
10.23 At low temperatures, say below 50 K, the thermal conductivity of a metal
is proportional to the absolute temperature, that is, k = aT , where a is a
constant with a numerical value that depends on the particular metal. Show
that the rate of heat flow through a rod of length L and cross-sectional area A
and whose ends are at temperatures T 1 and T 2 is given by Q =
a A
2L
(T 2
1 −T 2
2 ).
10.24 Find the radial flow of heat in a material of thermal conductivity placed
between two concentric spheres of radii r 1 and r 2 (r 1 < r 2 ) which are maintained at temperatures T 1 and T 2 (T 1 > T 2 ).