Advertisements
Advertisements
प्रश्न
Steam at 120°C is continuously passed through a 50 cm long rubber tube of inner and outer radii 1.0 cm and 1.2 cm. The room temperature is 30°C. Calculate the rate of heat flow through the walls of the tube. Thermal conductivity of rubber = 0.15 J s−1 m−1°C−1.
Advertisements
उत्तर
For steady conduction through a hollow cylinder:
`Q/t = (2pikL(T_1 - T_2))/ln(r^2/r^1)`
Substitute given values
k = 0.15J s−1m−1∘C−1
L = 50cm = 0.50m
T1 = 120∘C, T2 = 30∘C → ΔT = 90∘C
r1=1.0 cm = 0.010 m
r2 = 1.2cm = 0.012m
`Q/t = (2pi(0.15)(0.50)(90))/ln(0.012/0.010)`
2π ⋅ 0.15 ⋅ 0.50 ⋅ 90 = 2π ⋅ 6.75 = 42.41
ln`(0.012/0.010) = ln(1.2) = 0.1823`
`Q/t = 42.41/0.1823 =` 232.6 J/s
= 233 J/s
APPEARS IN
संबंधित प्रश्न
A tightly closed metal lid of a glass bottle can be opened more easily if it is put in hot water for some time. Explain.
A metal sheet with a circular hole is heated. The hole
Two identical rectangular strips, one of copper and the other of steel, are riveted together to form a bimetallic strip (acopper> asteel). On heating, this strip will
Find the ratio of the lengths of an iron rod and an aluminium rod for which the difference in the lengths is independent of temperature. Coefficients of linear expansion of iron and aluminium are 12 × 10–6 °C–1 and 23 × 10–6 °C–1 respectively.
In a room containing air, heat can go from one place to another
A steel frame (K = 45 W m−1°C−1) of total length 60 cm and cross sectional area 0.20 cm2, forms three sides of a square. The free ends are maintained at 20°C and 40°C. Find the rate of heat flow through a cross section of the frame.
On a winter day when the atmospheric temperature drops to −10°C, ice forms on the surface of a lake. (a) Calculate the rate of increase of thickness of the ice when 10 cm of the ice is already formed. (b) Calculate the total time taken in forming 10 cm of ice. Assume that the temperature of the entire water reaches 0°C before the ice starts forming. Density of water = 1000 kg m−3, latent heat of fusion of ice = 3.36 × 105 J kg−1and thermal conductivity of ice = 1.7 W m−1°C−1. Neglect the expansion of water of freezing.
A semicircular rod is joined at its end to a straight rod of the same material and the same cross-sectional area. The straight rod forms a diameter of the other rod. The junctions are maintained at different temperatures. Find the ratio of the heat transferred through a cross section of the semicircular rod to the heat transferred through a cross section of the straight rod in a given time.
Four identical rods AB, CD, CF and DE are joined as shown in following figure . The length, cross-sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperature T1, T2 and T3 respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.
There are two identical vessels filled with equal amounts of ice. The vessels are of different metals. If the ice melts in the two vessels in 20 and 35 minutes respectively, the ratio of the coefficients of thermal conductivity of the two metals is:
The coefficient of thermal conductivity depends upon ______.
We would like to prepare a scale whose length does not change with temperature. It is proposed to prepare a unit scale of this type whose length remains, say 10 cm. We can use a bimetallic strip made of brass and iron each of different length whose length (both components) would change in such a way that difference between their lengths remain constant. If αiron = 1.2 × 10−5/K and αbrass = 1.8 × 10−5/K, what should we take as length of each strip?
A cylinder of radius R made of material of thermal conductivity K1 is surrounded by a cylindrical shell of inner radius R and outer radius 3R made of a material of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. What is the effective thermal conductivity of the system?
In conduction, how does heat mainly travel through a solid rod kept with one end in a flame?
Why are metals like copper and aluminium called good conductors of heat?
At the molecular level, how is heat transferred in a solid during conduction?
