# Two metal rods $$1$$ and $$2$$ of same lengths have the same temperature difference between their ends. Their thermal conductivities are $${K}_1$$ and $${K}_2$$ and cross-sectional areas $${A}_{1}$$ and $${A}_{2},$$ respectively. If the rate of heat conduction in $$1$$ is four times that in $$2,$$ then: 1. $$K_1 A_1=4K_2 {A}_2$$ 2. $$K_1 {A}_1=2 {K}_2 {A}_2$$ 3. $$4 {K}_1{A}_1={K}_2 {A}_2$$ 4. $${K}_1 {A}_1={K}_2 {A}_2$$

Subtopic:  Conduction |
74%
From NCERT
NEET - 2013
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The density of water at $$20^\circ \text{C}$$ is $$998$$ kg/m3 and at $$40^\circ \text{C}$$ is $$992$$ kg/m3. The coefficient of volume expansion of water is:
1. $$3 \times 10^{-4} / ^\circ\text C$$
2. $$2 \times 10^{-4} / ^\circ\text C$$
3. $$6 \times 10^{-4} / ^\circ\text C$$
4. $$10^{-4} / ^\circ\text C$$
Subtopic:  Thermal Expansion |
71%
From NCERT
NEET - 2013
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A slab of stone with an area $$0.36~\text{m}^{2}$$${}^{}$ and thickness of $$0.1~\text{m}$$ is exposed on the lower surface to steam at $$100​​^{\circ}\mathrm{C}$$. A block of ice at $$0^{\circ}\mathrm{C}$$ rests on the upper surface of the slab. In one hour $$4.8~\text{kg}$$ of ice is melted. The thermal conductivity of the slab will be: (Given latent heat of fusion of ice $$= 3.36\times10^{5}~\text{JKg}^{-1}$$${}^{}$)
1. $$1.29~\text{J/m/s/}^{\circ}\text{C}$$
2. $$2.05~\text{J/m/s/}^{\circ}\text{C}$$
3. $$1.02~\text{J/m/s/}^{\circ}\text{C}$$
4. $$1.24~\text{J/m/s/}^{\circ}\text{C}$$

Subtopic:  Conduction |
58%
From NCERT
AIPMT - 2012
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A black body at 1227 °C emits radiations with maximum intensity at a wavelength of 5000 Å. If the temperature of the body is increased by 1000 °C, the maximum intensity will be observed at:

1. 4000 Å

2. 5000 Å

3. 6000 Å

4. 3000 Å

Subtopic:  Wien's Displacement Law |
57%
From NCERT
AIPMT - 2006
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A black body is at 727 °C. It emits energy at a rate that is proportional to:

1. $\left(727{\right)}^{2}$

2. $\left(1000{\right)}^{4}$

3. $\left(1000{\right)}^{2}$

4. $\left(727{\right)}^{4}$

80%
From NCERT
AIPMT - 2007
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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 of the earth (normal to the incident rays) at a distance from the centre of the sun is:
(where σ is Stefan’s constant.)

1. $\frac{4{\mathrm{\pi r}}^{2}{\mathrm{\sigma t}}^{4}}{{R}^{2}}$

2. $\frac{{r}^{2}\sigma \left(t+273{\right)}^{4}}{4\mathrm{\pi }{R}^{2}}$

3. $\frac{16{\pi }^{2}{r}^{2}{\mathrm{\sigma t}}^{4}}{{R}^{2}}$

4. $\frac{{r}^{2}\sigma \left(t+273{\right)}^{4}}{{R}^{2}}$

65%
From NCERT
AIPMT - 2007
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If the cold junction of a thermocouple is kept at 0 °C and the hot junction is kept at T °C, then the relation between neutral temperature (${\mathrm{T}}_{\mathrm{n}}$) and temperature of inversion (${\mathrm{T}}_{\mathrm{i}}$) is:

1. ${\mathrm{T}}_{\mathrm{n}}=\frac{{\mathrm{T}}_{\mathrm{i}}}{2}$

2. ${\mathrm{T}}_{\mathrm{n}}$= 2${\mathrm{T}}_{\mathrm{i}}$

3. ${\mathrm{T}}_{\mathrm{n}}$${\mathrm{T}}_{\mathrm{i}}$ - T

4. ${\mathrm{T}}_{\mathrm{n}}$= ${\mathrm{T}}_{\mathrm{i}}$ + T

Subtopic:  Calorimetry |
AIPMT - 2007
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On a new scale of temperature, which is linear and called the $$\mathrm{W}$$ scale, the freezing and boiling points of water are $$39^\circ ~\mathrm{W}$$and $$239^\circ ~\mathrm{W}$$ respectively. What will be the temperature on the new scale corresponding to a temperature of $$39^\circ ~\mathrm{C}$$ on the Celsius scale?
1. $$78^\circ ~\mathrm{C}$$
2. $$117^\circ ~\mathrm{W}$$
3. $$200^\circ ~\mathrm{W}$$
4. $$139^\circ ~\mathrm{W}$$

Subtopic:  Temperature and Heat |
83%
From NCERT
AIPMT - 2008
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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 $\frac{\mathrm{dQ}}{\mathrm{dt}}$ through the rod in a steady state is given by:

1. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KL}\left({\mathrm{T}}_{1}-{\mathrm{T}}_{2}\right)}{\mathrm{A}}$

2. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{K}\left({\mathrm{T}}_{1}-{\mathrm{T}}_{2}\right)}{\mathrm{LA}}$

3. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{KLA}\left({\mathrm{T}}_{1}-{\mathrm{T}}_{2}\right)$

4. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KA}\left({\mathrm{T}}_{1}-{\mathrm{T}}_{2}\right)}{\mathrm{L}}$

Subtopic:  Conduction |
89%
From NCERT
AIPMT - 2009
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A black body at $$227^{\circ}~\mathrm{C}$$ radiates heat at the rate of $$7~ \mathrm{cal-cm^{-2}s^{-1}}$$.  At a temperature of $$727^{\circ}~\mathrm{C}$$, the rate of heat radiated in the same units will be:
1. $$60$$
2. $$50$$
3. $$112$$
4. $$80$$

Subtopic:  Stefan-Boltzmann Law |
86%
From NCERT
AIPMT - 2009
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