A copper rod of \(88\) cm and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is:
\(\left(\alpha_{Cu}= 1.7\times10^{-5}~\text{K}^{-1}~\text{and}~\alpha_{Al}= 2.2\times10^{-5}~\text{K}^{-1}\right)\)
1. \(68~\text{cm}\)
2. \(6.8~\text{cm}\)
3. \(113.9~\text{cm}\)
4. \(88~\text{cm}\)

In which of the following phenomenon heat convection does not take place

1. land and sea breeze

2. boiling of water

3. heating of glass surface due to filament of the bulb

4. air around the furnace

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

A black body is at 727 °C. It emits energy at a rate that is proportional to:

1. $(727{)}^2$

2. $(1000{)}^4$

3. $(1000{)}^2$

4. $(727{)}^4$

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

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

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

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

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. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KL}({\mathrm{T}}_1-{\mathrm{T}}_2)}{\mathrm{A}}$

2. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{K}({\mathrm{T}}_1-{\mathrm{T}}_2)}{\mathrm{LA}}$

3. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{KLA}({\mathrm{T}}_1-{\mathrm{T}}_2)$

4. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KA}({\mathrm{T}}_1-{\mathrm{T}}_2)}{\mathrm{L}}$

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. \(80\)

The temperature of a body on the Kelvin scale is found to be x K. When it is measured by a Fahrenheit thermometer, it is found to be x$°$F, then the value of x is:
1. 40
2. 313
3. 574.25
4. 301.25

The graph AB shown in figure is a plot of the temperature of a body in degree Celsius and degree Fahrenheit. Then,