Advertisements
Advertisements
Question
Find the temperature of a blackbody if its spectrum has a peak at (a) λmax = 700 nm (visible), (b) λmax = 3 cm (microwave region) (c) λmax = 3 m (short radio waves). (Take Wien’s constant b = 2.897 × 10-3 m.K).
Advertisements
Solution
Given: (a) λmax = 700 nm = 700 × 10-9 m,
(b) λmax = 3 cm = 3 × 10-2 m,
(c) λmax = 3 cm,
b = 2.897 × 10-3 m.K.
∴ λmax T = b
(a) T = `"b"/lambda_"max"`
`= (2.897 xx 10^-3 "m"."K")/(700 xx 10^-9 "m")`
`= (2.897 xx 10^-3)/(7 xx 10^-7)`
= 0.4138 × 104
= 4138 K
(b) T = `"b"/lambda_"max"`
`= (2.897 xx 10^-3 "m"."K")/(3 xx 10^-2 "m")`
`= (2.879 xx 10^-1 "K")/3`
= 0.966 × 10-1 K
= 0.0966 K
(c) T = `"b"/lambda_"max"`
`= (2.897 xx 10^-3 "m.K")/(3 " m")`
= 0.966 × 10-3 K
APPEARS IN
RELATED QUESTIONS
Can we define the temperature of (a) vacuum, (b) a single molecule?
A gas is kept in an enclosure. The pressure of the gas is reduced by pumping out some gas. Will the temperature of the gas decrease by Charles's low?
Which of the following parameters is the same for molecules of all gases at a given temperature?
The average translational kinetic energy of air molecules is 0.040 eV (1 eV = 1.6 × 10−19J). Calculate the temperature of the air. Boltzmann constant k = 1.38 × 10−23 J K−1.
The condition of air in a closed room is described as follows. Temperature = 25°C, relative humidity = 60%, pressure = 104 kPa. If all the water vapour is removed from the room without changing the temperature, what will be the new pressure? The saturation vapour pressure at 25°C − 3.2 kPa.
The temperature and the dew point in an open room are 20°C and 10°C. If the room temperature drops to 15°C, what will be the new dew point?
Using figure, find the boiling point of methyl alcohol at 1 atm (760 mm of mercury) and at 0.5 atm.
If a = 0.72 and r = 0.24, then the value of tr is ______.
Answer in brief:
Compare the rms speed of hydrogen molecules at 127°C with rms speed of oxygen molecules at 27ºC given that molecular masses of hydrogen and oxygen are 2 and 32 respectively.
Explain, on the basis of the kinetic theory of gases, how the pressure of a gas changes if its volume is reduced at a constant temperature.
Calculate the ratio of the mean square speeds of molecules of a gas at 30 K and 120 K.
Two vessels A and B are filled with the same gas where the volume, temperature, and pressure in vessel A is twice the volume, temperature, and pressure in vessel B. Calculate the ratio of the number of molecules of the gas in vessel A to that in vessel B.
Energy is emitted from a hole in an electric furnace at the rate of 20 W when the temperature of the furnace is 727°C. What is the area of the hole? (Take Stefan’s constant σ to be 5.7 × 10-8 Js-1 m-2K-4.)
Calculate the energy radiated in one minute by a blackbody of surface area 200 cm2 at 127 °C (σ = 5.7 x 10-8 J m-2 s-1 K-4)
On what, the values of absorption coefficient, reflection coefficient, and transmission coefficient depend, in addition to the material of the object on which the radiation is an incident?
Why the temperature of all bodies remains constant at room temperature?
The average K.E. of hydrogen molecules at 27° C is E. The average K.E. at 627° C is ____________.
An ideal gas in a container of volume 500 cc is at a pressure of 2 × 105 N/m2. The average kinetic energy of each molecule is 6 × 10−21 J. The number of gas molecules in the container is ______.
Two molecules of a gas have speeds of 9 × 10 6 ms−1 and 1 × 106 ms−1, respectively. What is the root mean square speed of these molecules?
A gas mixture consists of molecules of types A, B and C with masses mA > mB > mC. Rank the three types of molecules in decreasing order of average K.E.
A gas mixture consists of molecules of types A, B and C with masses mA > mB > mC. Rank the three types of molecules in decreasing order of rms speeds.
An insulated container containing monoatomic gas of molar mass m is moving with a velocity vo. If the container is suddenly stopped, find the change in temperature.
Explain why there is no atmosphere on moon.
The Q-value of a nuclear reaction and kinetic energy of the projectile particle, KP are related as ______.
A proton, a deuteron and an α-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is ______.
When the temperature of an ideal gas is increased from 27°C to 227°C, its speed is changed from 400 ms-1 to vs, and Then vs is ______.
If a = 0. 72 and r = 0.24, then the value of t is ______.
Which of the following materials is diathermanous?
