Advertisements
Advertisements
प्रश्न
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
उत्तर
(a) the maximum intensity of radiation will be near the frequency 2v0
(c) the total energy emitted will increase by a factor of 16
From Wein's displacement law,
λmT = b ( a constant )
or `(cT)/(Vm) = b`
Here, T is the absolute temperature of the body.
So, as the temperature is doubled to keep the product on the left hand side constant, frequency is also doubled.
From Stefan's law, we know that the rate of energy emission is proportional to T4
This implies that total energy emitted will increase by a factor of (2)4, which is equal to 16.
APPEARS IN
संबंधित प्रश्न
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
Why is a white dress more comfortable than a dark dress in summer?
A solid at temperature T1 is kept in an evacuated chamber at temperature T2 > T1. The rate of increase of temperature of the body is proportional to
Two bodies A and B having equal surface areas are maintained at temperature 10°C and 20°C. The thermal radiation emitted in a given time by A and B are in the ratio
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.
A spherical ball A of surface area 20 cm2 is kept at the centre of a hollow spherical shell B of area 80 cm2. The surface of A and the inner surface of B emit as blackbodies. Both A and B are at 300 K. (a) How much is the radiation energy emitted per second by the ball A? (b) How much is the radiation energy emitted per second by the inner surface of B? (c) How much of the energy emitted by the inner surface of B falls back on this surface itself?
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 ______.
