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

A slab of stone with an area \(0.36~\text{m}^{2}\)${\mathrm{}}^{}$ and thickness of \(0.1~\text{m}\) is exposed on the lower surface to steam at \(100​​^\circ\text{C}.\)$$ A block of ice at \(0^{\circ}\text{C}\) rests on the upper surface of the slab. In one hour \(4.8~\text{kg}\) of ice is melted. The thermal conductivity of the slab will be:
(Given latent heat of fusion of ice \(= 3.36\times10^{5}~\text{JKg}^{-1}\)${\mathrm{}}^{}$)
1. \(1.29~\text{J/m/s/}^{\circ}\text{C}\)
2. \(2.05~\text{J/m/s/}^{\circ}\text{C}\)
3. \(1.02~\text{J/m/s/}^{\circ}\text{C}\)
4. \(1.24~\text{J/m/s/}^{\circ}\text{C}\)

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

The two ends of a rod of length \(L\) and a uniform cross-sectional area \(A\) are kept at two temperatures \(T_1\text{ and }T_2~ (T_1> T_2).\) The rate of heat transfer \(\dfrac{dQ}{dt}\) through the rod in a steady state is given by:

1. \(\dfrac{dQ}{dt} = \dfrac{KL \left(\right. T_{1} - T_{2} \left.\right)}{A}\)

2. \(\dfrac{dQ}{dt} = \dfrac{K \left(\right. T_{1} - T_{2} \left.\right)}{LA}\)

3. \(\dfrac{dQ}{dt} = KLA \left(\right. T_{1} - T_{2} \left.\right)\)

4. \(\dfrac{dQ}{dt} = \dfrac{KA \left(\right. T_{1} - T_{2} \left.\right)}{L}\)

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:

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:

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

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. $\frac{Q_1}{2}$