Two conducting slabs of heat conductivity \(K_{1} ~  \text{and}   ~K_{2}\) are joined as shown in fig. If the temperature at the ends of the slabs are \(\theta_{1}\  and\  \theta_{2} \ (\theta_{1}   >   \theta_{2} ),  \)then the final temperature \( \left(\theta\right)_{m} \)of the junction will be:

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. $\frac{Q_1}{2}$

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. \(\frac{K_2A_1}{S_2}=\frac{K_1A_2}{S_1}\)

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. $4/3$ $\mathrm{K}$

The temperature of inversion of a thermocouple is 620ºC and the neutral temperature is 300ºC. What is the temperature of the cold junction:

1. 40ºC

2. 20ºC

3. 320ºC

4. –20ºC

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 the most heat: