# If the radius of a star is $$R$$ and it acts as a black body, what would be the temperature of the star at which the rate of energy production is $$Q$$? 1. $$\frac{Q}{4\pi R^2\sigma}$$ 2. $$\left(\frac{Q}{4\pi R^2\sigma}\right )^{\frac{-1}{2}}$$ 3. $$\left(\frac{4\pi R^2 Q}{\sigma}\right )^{\frac{1}{4}}$$ 4. $$\left(\frac{Q}{4\pi R^2 \sigma}\right)^{\frac{1}{4}}$$

Subtopic:  Stefan-Boltzmann Law |
83%
From NCERT
AIPMT - 2012
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

Liquid oxygen at $$50$$ K is heated up to $$300$$ K at a 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 2 3 4
Subtopic:  Calorimetry |
80%
From NCERT
AIPMT - 2012
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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 at the same time?

1. Q /4

2. Q/16

3. 2Q

4. Q/2

Subtopic:  Conduction |
60%
From NCERT
AIPMT - 2010
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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: (Where $$\sigma$$ is Stefan’s constant):
1. $$\frac{\sigma r^{2}T^{4}}{R^{2}}$$

2. $$\frac{\sigma r^{2}T^{4}}{4 \pi R^{2}}$$

3. $$\frac{\sigma r^{2}T^{4}}{R^{4}}$$

4. $$\frac{4\pi\sigma r^{2}T^{4}}{R^{2}}$$

Subtopic:  Stefan-Boltzmann Law |
63%
From NCERT
AIPMT - 2010
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints

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
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

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. $\left(727{\right)}^{4}$