Advertisements
Advertisements
प्रश्न
A body cools down from 50°C to 45°C in 5 mintues and to 40°C in another 8 minutes. Find the temperature of the surrounding.
उत्तर
Let the temperature of the surroundings be T0°C.
Case 1:
Initial temperature of the body = 50°C
Final temperature of the body = 45°C
Average temperature = 47.5 °C
Difference in the temperatures of the body and its surrounding = (47.5 − T)°C
Rate of fall of temperature = `(Deltat)/t = (5)/5 = 1°`C/min
By Newton's law of cooling,
`(dt)/dt = -K [T_{avg} - T_0 ]`
1 = -K [47.5 - t0]........... (i)
Case 2:
Initial temperature of the body = 45°C
Final temperature of the body = 40°C
Average temperature = 42.5 °C
Difference in the temperatures of the body and its surrounding = (42.5 − T0)°C
Rate of fall of temperature = `(DeltaT)/t = 5/8 = 5/8`°C/min
From Newton,s law of cooling,
`(dT)/(dt) = -K[T_{avg} - T_0 ]`
0.625 = -K [42.5 - T0] ........ (2)
Dividing (1) by (2),
`1/0.625 = (47.5 - T_0)/(42.5 - T_0)`
⇒ 42.5 - T_0 = 29.68 - 0.625T
⇒ T0 = 34° C
APPEARS IN
संबंधित प्रश्न
Draw a neat labelled diagram for Ferry's perfectly black body.
Let 'p' and 'E' denote the linear momentum and energy of emitted photon respectively. If the wavelength of incident radiation is increased ___ .
(a) both p and E increase
(b) p increases and E decreases
(c) p decreases and E increases
(d) both p and E decrease.
Show graphical representation of energy distribution spectrum of perfectly black body.
The wavelength range of thermal radiation is
(A) from 4000 Å to 7000 Å
(B) from 7700 Å to 4 x 106 Å
(C) from 106 Å to 108 Å
(D) from 4 x 10-12 Å to 4 x 108 Å
Find the wavelength at which a black body radiates maximum energy, if its temperature is 427°C.
(Wein’s constant b = 2.898 × 10-3 mK)
(A) 0.0414 × 10-6m
(B) 4.14 × 10-6m
(C) 41.4 × 10-6m
(D) 414 × 10-6m
Explain black body radiation spectrum in terms of wavelength
What is perfectly black body ? Explain Ferry’s black body.
Does a body at 20°C radiate in a room, where the room temperature is 30°C? If yes, why does its temperature not fall further?
The thermal radiation emitted by a body is proportional to Tn where T is its absolute temperature. The value of n is exactly 4 for
A blackbody does not
(a) emit radiation
(b) absorb radiation
(c) reflect radiation
(d) refract radiation
The normal body-temperature of a person is 97°F. Calculate the rate at which heat is flowing out of his body through the clothes assuming the following values. Room temperature = 47°F, surface of the body under clothes = 1.6 m2, conductivity of the cloth = 0.04 J s−1 m−1°C−1, thickness of the cloth = 0.5 cm.
A cubical block of mass 1.0 kg and edge 5.0 cm is heated to 227°C. It is kept in an evacuated chamber maintained at 27°C. Assuming that the block emits radiation like a blackbody, find the rate at which the temperature of the block will decrease. Specific heat capacity of the material of the block is 400 J Kg-1 K-1.
One end of a rod of length 20 cm is inserted in a furnace at 800 K. The sides of the rod are covered with an insulating material and the other end emits radiation like a blackbody. The temperature of this end is 750 K in the steady state. The temperature of the surrounding air is 300 K. Assuming radiation to be the only important mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of the rod. Stefan constant σ = 6.0 × 10−8 W m−2 K−4.
A metal ball of mass 1 kg is heated by means of a 20 W heater in a room at 20°C. The temperature of the ball becomes steady at 50°C. (a) Find the rate of loss of heat to the surrounding when the ball is at 50°C. (b) Assuming Newton's law of cooling, calculate the rate of loss of heat to the surrounding when the ball rises 30°C. (c) Assume that the temperature of the ball rises uniformly from 20°C to 30°C in 5 minutes. Find the total loss of heat to the surrounding during this period. (d) Calculate the specific heat capacity of the metal.
A hot body placed in a surrounding of temperature θ0 obeys Newton's law of cooling `(d theta)/(dt) = -K(theta - theta_0)` . Its temperature at t = 0 is θ1. The specific heat capacity of the body is sand its mass is m. Find (a) the maximum heat that the body can lose and (b) the time starting from t = 0 in which it will lose 90% of this maximum heat.
