The two ends of a metal rod are maintained at temperatures \(100^{\circ}\mathrm{C}\) and \(110^{\circ}\mathrm{C}\). The rate of heat flow in the rod is found to be 4.0 J/s. If the ends are maintained at temperatures \(200^{\circ}\mathrm{C}\) and \(210^{\circ}\mathrm{C}\), the rate of heat flow will be:
1. 44.0 J/s
2. 16.8 J/s
3. 8.0 J/s
4. 4.0 J/s

Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod has the same length. The left and right ends are kept at \(0^{\circ}\text{C}~\text{and}~90^{\circ}\text{C},\) respectively. The temperature at the junction of the three rods will be:

           
1. \(45^{\circ}\text{C}\)
2. \(60^{\circ}\text{C}\)
3. \(30^{\circ}\text{C}\)
4. \(20^{\circ}\text{C}\)

Mud houses are cooler in the summer and warmer in the winter because:

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

Two rods, A and B, of different materials having the same cross-sectional area are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:

1. $\frac{K_1+K_2}{2}$
2. $\frac{3\left(K_1+K_2\right)}{2}$
3. $K_1+K_2$
4. $2\left(K_1+K_2\right)$

Four rods of the same material with different radii \(r\) and length \(l\) are used to connect two heat reservoirs at different temperatures. In which of the following cases is the heat conduction fastest?
1. \(r = \frac{1}{3}~\text{cm}, l = \frac{1}{9}~\text{cm}\)
2. \(r =3~\text{cm}, l =9~\text{cm}\)
3. \(r =4~\text{cm}, l =8~\text{cm}\)
4. \(r =1~\text{cm}, l =1~\text{cm}\)

When two ends of a rod wrapped with cotton are maintained at different temperatures and, after some time, every point of the rod attains a constant temperature, then:

Three rods made of the same material, having the same cross-sectional area but different lengths 10 cm, 20 cm and 30 cm are joined as shown. The temperature of the junction will be:-

   
1. \(10.8^{\circ}\mathrm{C}\)
2. \(14.6^{\circ}\mathrm{C}\)
3. \(16.4^{\circ}\mathrm{C}\)
4. \(18.2^{\circ}\mathrm{C}\)

Two rods (one semi-circular and the other straight) of the same material and of the same cross-sectional area are joined as shown in the figure. Points \(A\) and \(B\) are maintained at different temperatures. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross-section of a straight rod at any given point in time will be:
                 
1. \(2:\pi\)
2. \(1:2\)
3. \(\pi:2\)
4. \(3:2\)

One likes to sit in the sunshine in the winter season, because: