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).
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
Do you expect the gas in a cooking gas cylinder to obey the ideal gas equation?
Comment on the following statement: the temperature of all the molecules in a sample of a gas is the same.
Consider a gas of neutrons. Do you expect it to behave much better as an ideal gas as compared to hydrogen gas at the same pressure and temperature?
Is it possible to boil water at room temperature, say 30°C? If we touch a flask containing water boiling at this temperature, will it be hot?
The pressure of an ideal gas is written as \[P = \frac{2E}{3V}\] . Here E refers to
Which of the following quantities is the same for all ideal gases at the same temperature?
(a) The kinetic energy of 1 mole
(b) The kinetic energy of 1 g
(c) The number of molecules in 1 mole
(d) The number of molecules in 1 g
Find the number of molecules of an ideal gas in a volume of 1.000 cm3 at STP.
During an experiment, an ideal gas is found to obey an additional law pV2 = constant. The gas is initially at a temperature T and volume V. Find the temperature when it expands to a volume 2V.
Use R = 8.3 J K-1 mol-1
An ideal gas is kept in a long cylindrical vessel fitted with a frictionless piston of cross-sectional area 10 cm2 and weight 1 kg in figure. The vessel itself is kept in a big chamber containing air at atmospheric pressure 100 kPa. The length of the gas column is 20 cm. If the chamber is now completely evacuated by an exhaust pump, what will be the length of the gas column? Assume the temperature to remain constant throughout the process.
Using figure, find the boiling point of methyl alcohol at 1 atm (760 mm of mercury) and at 0.5 atm.
A glass contains some water at room temperature 20°C. Refrigerated water is added to it slowly. when the temperature of the glass reaches 10°C, small droplets condense on the outer surface. Calculate the relative humidity in the room. The boiling point of water at a pressure of 17.5 mm of mercury is 20°C and at 8.9 mm of mercury it is 10°C.
Answer in brief:
What will happen to the mean square speed of the molecules of a gas if the temperature of the gas increases?
Answer in brief:
A gas in a cylinder is at pressure P. If the masses of all the molecules are made one-third of their original value and their speeds are doubled, then find the resultant pressure.
At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? (Molecular masses of oxygen and helium are 32 and 4 respectively).
Answer in brief:
Compare the rms speed of hydrogen molecules at 127ºC with rms speed of oxygen molecules at 27ºC given that molecular masses of hydrogen and oxygen are 2 and 32 respectively.
If the density of oxygen is 1.44 kg/m3 at a pressure of 105 N/m2, find the root mean square velocity of oxygen molecules.
Find the kinetic energy of 5 litres of a gas at STP, given the standard pressure is 1.013 × 105 N/m2.
The emissive power of a sphere of area 0.02 m2 is 0.5 kcal s-1m-2. What is the amount of heat radiated by the spherical surface in 20 seconds?
Compare the rates of emission of heat by a blackbody maintained at 727°C and at 227°C, if the black bodies are surrounded by an enclosure (black) at 27°C. What would be the ratio of their rates of loss of heat?
Under which condition laws of Boyle, Charles, and Gay-Lussac are valid?
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?
What is the microscopic origin of temperature?
The average translational kinetic energy of a molecule in a gas becomes equal to 0.49 eV at a temperature about (Boltzmann constant = 1.38 x 10-23 JK-1) ____________.
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.
For a particle moving in vertical circle, the total energy at different positions along the path ______.
When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle is n, then the frequency of the kinetic energy is ______.
According to the kinetic theory of gases, at a given temperature, molecules of all gases have the same ______.
At what temperature will therms velocity of a gas be four times its value at STP?
2000 calories of radiant heat is incident on a body. If the body absorbs 550 calories of heat, find the coefficient of emmission of the body.
