Advertisements
Advertisements
Question
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?
Advertisements
Solution
Data: T1 = 273 + 727 = 1000 K,
T2 = 273 + 227 = 500 K,
T0 = 273 + 27 = 300 K
(i) The rate of emission of heat, `"dQ"/"dt" = sigma"AT"^4`.
We assume that the surface area A is the same for the two bodies.
`∴ ("dQ"//"dt")_1/("dQ"//"dt")_2 = "T"_1^4/"T"_2^4 = ("T"_1/"T"_2)^4`
`= (1000/500)^4 = 2^4 = 16`
(ii) The rate of loss of heat, `"dQ'"/"dt" = sigma"A" ("T"^4 - "T"_0^4)`
`∴ ("dQ'"//"dt")_1/("dQ'"//"dt")_2 = ("T"_1^4 - "T"_0^4)/("T"_2^4 - "T"_0^4)`
`= (10^12 - 81 xx 10^8)/(625 xx 10^8 - 81 xx 10^8)`
`= ((10000 - 81) xx 10^8)/(544 xx 10^8)`
`= 9919/544 = 18.23`
APPEARS IN
RELATED QUESTIONS
When we place a gas cylinder on a van and the van moves, does the kinetic energy of the molecules increase? Does the temperature increase?
Do you expect the gas in a cooking gas cylinder to obey the ideal gas equation?
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?
If the molecules were not allowed to collide among themselves, would you expect more evaporation or less evaporation?
Which of the following parameters is the same for molecules of all gases at a given temperature?
The mean square speed of the molecules of a gas at absolute temperature T is proportional to
The process on an ideal gas, shown in figure, is
Find the number of molecules of an ideal gas in a volume of 1.000 cm3 at STP.
At what temperature the mean speed of the molecules of hydrogen gas equals the escape speed from the earth?
Use R = 8.314 JK-1 mol-1
0.040 g of He is kept in a closed container initially at 100.0°C. The container is now heated. Neglecting the expansion of the container, calculate the temperature at which the internal energy is increased by 12 J.
Use R = 8.3 J K-1 mol-1
One mole of an ideal gas undergoes a process `P = (P_0)/(1+(V/V_0)^2` where `p_0` and `V_0` are constants . Find the temperature of the gas when `V=V_0` .
Figure shows a cylindrical tube of radius 5 cm and length 20 cm. It is closed by a tight-fitting cork. The friction coefficient between the cork and the tube is 0.20. The tube contains an ideal gas at a pressure of 1 atm and a temperature of 300 K. The tube is slowly heated and it is found that the cork pops out when the temperature reaches 600 K. Let dN denote the magnitude of the normal contact force exerted by a small length dlof the cork along the periphery (see the figure). Assuming that the temperature of the gas is uniform at any instant, calculate `(dN)/(dt)`.
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.
Figure shows two rigid vessels A and B, each of volume 200 cm3, containing an ideal gas (Cv = 12.5 J K−1 mol−1). The vessels are connected to a manometer tube containing mercury. The pressure in both the vessels is 75 cm of mercury and the temperature is 300 K. (a) Find the number of moles of the gas in each vessel. (b) 5.0 J of heat is supplied to the gas in vessel A and 10 J to the gas in vessel B. Assuming there's no appreciable transfer of heat from A to B, calculate the difference in the heights of mercury in the two sides of the manometer. Gas constant, R = 8.3 J K−1 mol−1.
If a = 0.72 and r = 0.24, then the value of tr is ______.
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.)
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).
The number of degrees of freedom, for the vibrational motion of a polyatomic molecule, depends on the ______
The power radiated by a perfect blackbody depends only on its ______
Above what temperature, all bodies radiate electromagnetic radiation?
If the density of nitrogen is 1.25 kg/m3 at a pressure of 105 Pa, find the root mean square velocity of nitrogen molecules.
The average translational kinetic energy of gas molecules depends on ____________.
What is the microscopic origin of temperature?
Explain in detail the kinetic interpretation of temperature.
The average K.E. of hydrogen molecules at 27° C is E. The average K.E. at 627° C is ____________.
Assuming the expression for the pressure exerted by the gas on the wall of the container, it can be shown that pressure is ______.
If a = 0. 72 and t = 0.04, then the value of r is ______.
Which of the following materials is diathermanous?
