A cup of coffee cools from \(90^{\circ}\mathrm{C}\) $\mathrm{to}$ \(80~^{\circ}\mathrm{C}\) in t minutes, when the room temperature is \(20^{\circ}\mathrm{C}\)$\mathrm{}$. The time taken by a similar cup of coffee to cool from \(80^{\circ}\mathrm{C}\) $\mathrm{to}$ \(60^{\circ}\mathrm{C}\) at room temperature same at \(20^{\circ}\mathrm{C}\) is:
1. \(\frac{10}{13}t\) 
2. \(\frac{5}{13}t\)
3. \(\frac{13}{10}t\)
4. \(\frac{13}{5}t\)

Consider a compound slab consisting of two different materials having equal thicknesses and thermal conductivities K and 2K, respectively. The equivalent thermal conductivity of the slab will be:

1. $2/6$ $\mathrm{K}$

2. $\sqrt{2}$ $\mathrm{K}$

3. $3\mathrm{K}$

4. $4/3$ $\mathrm{K}$

We consider the radiation emitted by the human body. Which of the following statements is true:
 

A cylindrical rod has temperatures ${\mathrm{T}}_1$ $\mathrm{and}$ ${\mathrm{T}}_2$ at its ends. The rate of flow of heat is $Q_1$ cal/sec. If all the linear dimensions are doubled while keeping the temperature constant, then the rate of flow of heat $Q_2$ will be:

1. $4Q_1$

2. $2Q_1$

3. $\frac{Q_1}{4}$

4. $\frac{Q_1}{2}$

A black body has a wavelength ${\lambda }_m$ corresponding to maximum energy at 2000 K. Its wavelength corresponding to maximum energy at 3000 K will be:

1. $\frac{3}{2}{\lambda }_m$

2. $\frac{2}{3}{\lambda }_m$

3. $\frac{16}{81}{\lambda }_m$

4. $\frac{81}{16}{\lambda }_m$

Unit of Stefan's constant is:

1. Watt-m²-K⁴

2. Watt-m²/K⁴

3. Watt/m²–K

4. Watt/m² K⁴

Consider two rods of the same length and different specific heats \((S_1,S_2)\) conductivities \((K_1,K_2)\) and area of cross-sections \((A_1,A_2)\) and both having temperature \(T_1\) and \(T_2\) at their ends. If the rate of loss of heat due to conduction is equal, then:
1. \(K_1A_1=K_2A_2\)
2. \(\frac{K_1A_1}{S_1}=\frac{K_2A_2}{S_2}\)
3. \(K_2A_1=K_1A_2\)
4. \(\frac{K_2A_1}{S_2}=\frac{K_1A_2}{S_1}\)

For a black body at a temperature of 727ºC, its radiating power is 60 watts and the temperature of the surroundings is 227ºC. If the temperature of the black body is changed to 1227ºC then its radiating power will be:

1. 304 W

2. 320 W

3. 240 W

4. 120 W

Which of the following is closest to an ideal black body?

Wien's displacement law expresses the relation between: