The rectangular surface of area 8cm × 4cm of a black body at temperature 127°C emits energy E per second. If the length and breadth are reduced to half of the initial value and the temperature is raised to 327°C, the rate of emission of energy becomes

⁸¹⁄₁₆E
⁸¹⁄₁₆E
⁹⁄₁₆E
⁸¹⁄₆₄E

Solution

E = σ × area × T⁴; T increases by a factor ³⁄₂.

Area increases by a factor ¹⁄₄.

A beaker contains 200 g of water. The heat capacity of beaker is equal to that 20 g of water. The initial temperature of water in the beaker is 20°C . If 440 g of hot water at 92°C is poured in, the final temperature, neglecting radiation loss, will be

58°C
68°C
73°C
78°C

Solution

Heat capacity of cold : hot =1 : 2

So final temp. is ¹⁄₃ × (2 × 92 + 1 × 20) = 68°C

5 kg of water at 10°C is added to 10 kg of water at 40°C.Neglecting heat capacity of vessel and other losses, the equilibrium temperature will be

30°C
25°C
35°C
33°C

Solution

Mass ratio 1 : 2; hence ΔT ratio 2 : 1. Therefore equilibrium temp is 30°C.

If a liquid is heated in weightlessness, the heat is transmitted through

conduction
convection
radiation
None of these, because the liquid cannot be heated in weightlessness.

Solution

In condition of weightlessness, convection is not possible.

Which of the following circular rods, (given radius r and length l) each made of the same material and whose ends are maintained at the same temperature will conduct most heat?

r = 2r₀; l = 2l₀
r = 2r₀; l = l₀
r = r₀; l = 2l₀
r = r₀; l = l₀

Solution

Which of the following graph correctly represents the relation between ln E and ln T where E is the amount of radiation emitted perunit time from unit area of body and T is the absolute temperature

Solution

We know

E = eT⁴ ⇒ ln E = ln e + 4 ln T

∴ ln e is negative

because e < 1

A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

Ec
2E/c
E/c
E/c²

Solution

Momentum of photon = ^E⁄_C

Change in momentum = ^2E⁄_C

momentum transferred to the surface(the photon will reflect with same magnitude of momentum in opposite direction).

A partition wall has two layers A and B, in contact, each made of a different material. They have the same thickness but the thermal conductivity of layer A is twice that of layer B. If the steady state temperature difference across the wall is 60 K,then the corresponding difference across the layer A is

10 K
20 K
30 K
40 K

Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in 20 min and 35 min, respectivley. The ratio of coefficients of thermal conduction of the metals is

4 : 7
7 : 4
25 : 16
16 : 25

Solution

Two identical rods of copper and iron are coated with wax uniformly. When one end of each is kept at temperature of boiling water, the length upto which wax melts are 8.4 cm amd 4.2 cm, respectively. If thermal conductivity of copper is 0.92, then thermal conductivity of iron is x

0.23
0.46
0.115
0.69

Solution

Use \(\frac{K_{1}}{K_{2}}=\frac{\iota _{1}^{2}}{\iota _{2}^{2}}\)

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