Advertisements
Advertisements
Question
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?
Advertisements
Solution
Given:
Surface area of the spherical ball, SA = 20 cm2 = 20 × 10 -4 m-2
Surface area of the spherical shell, SB = 80 cm2 = 80 × 10-4 m2
Temperature of the spherical ball, TA = 300 K
Temperature of the spherical shell, TB = 300 K
Radiation energy emitted per second by the spherical ball A is given by
EA = σSATA4
⇒EA 6.0 ×10-8× 20 × 10-4 × (300)4
⇒EA = 0.97 J
Radiation energy emitted per second by the inner surface of the spherical shell B is given by
EB = σ SBTB4
⇒ EB = 6.0 ×10 -8 × 80 × 10-4 × (300)4
⇒ EB = 3.76 J ≈ 3.8 J
Energy emitted by the inner surface of B that falls back on its surface is given by
E = EB - EA = 3.76 - 0.94
⇒ E = 2.82 J
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
Standing in the sun is more pleasant on a cold winter day than standing in shade. Is the temperature of air in the sun considerably higher than that of the air in shade?
Cloudy nights are warmer than the nights with clean sky. Explain
Why is a white dress more comfortable than a dark dress in summer?
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
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.
Calculate the amount of heat radiated per second by a body of surface area 12 cm2 kept in thermal equilibrium in a room at temperature 20°C. The emissivity of the surface = 0.80 and σ = 6.0 × 10−8 W m−2 K−4.
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?
Why are cooking utensils like pans made of metal but fitted with plastic or wooden handles?
A perfect black body has an emissivity value of ______.
Thermal radiation is described as a two-step process. Which of the following correctly identifies both steps in the correct order?
Which of the following properties is shared by both thermal radiation and visible light?
