Advertisements
Advertisements
Question
A cylindrical rod of length 50 cm and cross sectional area 1 cm2 is fitted between a large ice chamber at 0°C and an evacuated chamber maintained at 27°C as shown in the figure. Only small portions of the rod are inside the chamber and the rest is thermally insulated from the surrounding. The cross section going into the evacuated chamber is blackened so that it completely absorbs any radiation falling on it. The temperature of the blackened end is 17°C when steady state is reached. Stefan constant σ = 6 × 10−8 W m−2 K−4. Find the thermal conductivity of the material of the rod.
Advertisements
Solution
Length, l = 50 cm
Cross sectional area, A =1 cm2
Stefan's constant, σ = 6 × 10−8 W m−2 K−4
Temperature of the blackened end = 17°C
Temperature of the chamber = 27°C
Temperature of one end of the rod = 0°C
According to Stefan's law,
`(DeltaQ)/(Deltat) = ε. A σ (T_2^4 - T_1^4)`
`(DeltaQ)/(Deltat.A) =ε σ (T_2^4 - T_1^4) `
`(DeltaQ)/(Deltat.A) = 1xx6xx10^-s ((300)^4 - (290)^4)`
= 6 × 10.3 .... (1)
Also , (Delta Q)/(Delta t)` = `(KA(T_1 - T_2))/l` ........(2)
From (1) and (2),
6 × 10.3 = `(K × 17)/0.5`
k = 1.8 w/ °C
APPEARS IN
RELATED QUESTIONS
Explain why an optical pyrometer (for measuring high temperatures) calibrated for an ideal black body radiation gives too low a value for the temperature of a red hot iron piece in the open but gives a correct value for the temperature when the same piece is in the furnace
Explain why the earth without its atmosphere would be inhospitably cold
Why does blowing over a spoonful of hot tea cools it? Does evaporation play a role? Does radiation play a role?
Two identical metal balls one at T1 = 300 K and the other at T2 = 600 K are kept at a distance of 1 m in a vacuum. Will the temperatures equalise by radiation? Will the rate of heat gained by the colder sphere be proportional to `t_2^4 - t_1^4` as may be expected from the Stefan's law?
Cloudy nights are warmer than the nights with clean sky. Explain
A heated body emits radiation which has maximum intensity near the frequency v0. The emissivity of the material is 0.5. If the absolute temperature of the body is doubled.
(a) the maximum intensity of radiation will be near the frequency 2v0
(b) the maximum intensity of radiation will be near the frequency v0/2
(c) the total energy emitted will increase by a factor of 16
(d) the total energy emitted will increase by a factor of 8
A solid sphere and a hollow sphere of the same material and of equal radii are heated to the same temperature.
(a) Both will emit equal amount of radiation per unit time in the biginning
(b) Both will absorb equal amount of radiation from the surrounding in the biginning.
(c) The initial rate of cooling (dT/dt) will be the same for the two spheres
(d) The two spheres will have equal temperature at any instant
The left end of a copper rod (length = 20 cm, area of cross section = 0.20 cm2) is maintained at 20°C and the right end is maintained at 80°C. Neglecting any loss of heat through radiation, find (a) the temperature at a point 11 cm from the left end and (b) the heat current through the rod. Thermal conductivity of copper = 385 W m−1°C−1.
Assume that the total surface area of a human body is 1.6 m2 and that it radiates like an ideal radiator. Calculate the amount of energy radiated per second by the body if the body temperature is 37°C. Stefan constant σ is 6.0 × 10−8 W m−2 K−4.
A solid aluminium sphere and a solid copper sphere of twice the radius are heated to the same temperature and are allowed to cool under identically surrounding temperatures. Assume that the emissivity of both the spheres in the same. Find the ratio of (a) the rate of heat loss from the aluminium sphere to the rate of heat loss from the copper sphere and (b) the rate of fall of temperature of the aluminium sphere to the rate of fall of temperature of the copper sphere. The specific heat capacity of aluminium = 900 J kg−1°C−1 and that of copper = 390 J kg−1°C−1. The density of copper = 3.4 times the density of aluminium.
Wein's constant is 2892 × 10-6 SI unit and the value of λm for moon is 14.46 micron. The surface temperature of moon is ______.
A student says, "Heat from the Sun reaches Earth because air carries it across space." Which statement best explains why this is incorrect?
You place your hands near a burning candle and feel warmth on both sides of the flame. What does this observation mainly show?
Which statement best describes thermal radiation from everyday objects like trees, roads, and buildings at night?
Two identical metal tins with water are kept in sunlight. One is black and the other shiny. Why does water in the black tin become hotter?
