Advertisements
Advertisements
प्रश्न
A cubical box of volume 216 cm3 is made up of 0.1 cm thick wood. The inside is heated electrically by a 100 W heater. It is found that the temperature difference between the inside and the outside surface is 5°C in steady state. Assuming that the entire electrical energy spent appears as heat, find the thermal conductivity of the material of the box.
Advertisements
उत्तर
Volume of the cube, V = a3 = 216 cm3
Edge of the cube, a = 6 cm
Surface area of the cube = 6a2
= 6 (6 × 10−2)2
= 216 × 10−4 m2
Thickness, l = 0.1 cm = 0.1 × 10–2 m
Temperature difference, Δ T = 5°C
The inner surface of the cube is heated by a 100 W heater.
∴ Power, P = 100 W
Power = Energy per unit time
∴ Rate of flow of heat inside the cube, R = 100 J/s
Rate of flow of heat is given by
`(DeltaQ)/(Deltat) = (DeltaT)/(l/(KA)`
`100 = Kxx216xx10^-4xx5/(0.1xx10^-2)`
`K = 0.9259 ` W/ m° C
APPEARS IN
संबंधित प्रश्न
A metal sheet with a circular hole is heated. The hole
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
One end of a steel rod (K = 46 J s−1 m−1°C−1) of length 1.0 m is kept in ice at 0°C and the other end is kept in boiling water at 100°C. The area of cross section of the rod is 0.04 cm2. Assuming no heat loss to the atmosphere, find the mass of the ice melting per second. Latent heat of fusion of ice = 3.36 × 105 J kg−1.
Following Figure shows water in a container having 2.0 mm thick walls made of a material of thermal conductivity 0.50 W m−1°C−1. The container is kept in a melting-ice bath at 0°C. The total surface area in contact with water is 0.05 m2. A wheel is clamped inside the water and is coupled to a block of mass M as shown in the figure. As the block goes down, the wheel rotates. It is found that after some time a steady state is reached in which the block goes down with a constant speed of 10 cm s−1 and the temperature of the water remains constant at 1.0°C. Find the mass M of the block. Assume that the heat flows out of the water only through the walls in contact. Take g = 10 m s−2.
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.
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.
Following figure shows two adiabatic vessels, each containing a mass m of water at different temperatures. The ends of a metal rod of length L, area of cross section A and thermal conductivity K, are inserted in the water as shown in the figure. Find the time taken for the difference between the temperatures in the vessels to become half of the original value. The specific heat capacity of water is s. Neglect the heat capacity of the rod and the container and any loss of heat to the atmosphere.
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 thin rod having length L0 at 0°C and coefficient of linear expansion α has its two ends maintained at temperatures θ1 and θ2, respectively. Find its new length.
According to Stefan’s law of radiation, a black body radiates energy σT4 from its unit surface area every second where T is the surface temperature of the black body and σ = 5.67 × 10–8 W/m2K4 is known as Stefan’s constant. A nuclear weapon may be thought of as a ball of radius 0.5 m. When detonated, it reaches temperature of 106 K and can be treated as a black body.
- Estimate the power it radiates.
- If surrounding has water at 30°C, how much water can 10% of the energy produced evaporate in 1s? [Sw = 4186.0 J/kg K and Lv = 22.6 × 105 J/kg]
- If all this energy U is in the form of radiation, corresponding momentum is p = U/c. How much momentum per unit time does it impart on unit area at a distance of 1 km?
As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm2 for each plate. The equivalent thermal conductivity of the compound plate is `(1+5/alpha)`K, then the value of a will be ______.
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?
Which of the following is a correct example of a bad conductor of heat used in daily life to reduce heat loss or gain?
During conduction along a metal rod, which part becomes hot first, and why?
