Thermal Properties of Matter · Question 26

If the radius of a star is R and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is Q?

1. Q4 2
2. ( Q4 2 )-1/2
3. ( 4 2Q )1/4
4. ( Q4 2 )1/4

Liquid oxygen at 50 K is heated to 300 K at constant pressure of 1 atm. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time ?

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod, when placed in thermal contact with the two reservoirs in time t?

1. Q4
2. Q16
3. 2Q
4. Q2

The total radiant energy per unit area, normal to the direction of incidence, received at a distance R from the centre of a star of radius r, whose outer surface radiates as a black body at a temperature T K is given by

1. 2T4R2
2. 2T44 2
3. 2T4R4
4. 4 2T4R2

Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t C, the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is where is the Stefan's constant.

1. r2 (t + 273)44 2
2. 16 2r2 4R2
3. r2 (t + 273)4R2
4. 4 2 4R2

A black body at 227 C radiates heat at the rate of 7 cal/cm2 s. At a temperature of 727 C, the rate of heat radiated in the same units will be

1. 50
2. 112
3. 80
4. 60

The two ends of a rod of length L and a uniform cross-sectional area A are kept at two temperatures T1 and T2 (T1 > T2). The rate of heat transfer, dQdt through the rod in a steady state is given by :

1. dQdt = k(T1 - T2)LA
2. dQdt = kLA(T1 - T2)
3. dQdt = kA(T1 - T2)L
4. dQdt = kL(T1 - T2)A

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are 39 and 239 respectively. What will be the temperature on the new scale, corresponding to a temperature of 39 on the Celsius scale ?

1. 200
2. 139
3. 78
4. 117

Assuming the sun to have a spherical outer surface of radius r, radiating like a black body at temperature t C, the power received by a unit surface, (normal to the incident rays) at a distance R from the centre of the sun is where is the Stefan's constant.

1. r2 (t+273)44 2
2. 16 2r2 4R2
3. r2 (t+273)4R2
4. 4 2 4R2

A black body is at 727 . It emits energy at a rate which is proportional to

1. (1000)4
2. (1000)2
3. (727)4
4. (727)2