Q. No.Rods \(x\) and \(y\) of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points \(A\) and \(F\) are maintained at \(100^\circ\text{C}\) and \(40^\circ\text{C}\) respectively. Given the thermal conductivity of rod \(x\) is three times of that of rod \(y\), the temperature at junction points \(B\) and \(E\) are (close to):
1. \(89^\circ\text{C}\) and \(73^\circ\text{C}\) respectively
2. \(80^\circ\text{C}\) and \(60^\circ\text{C}\) respectively
3. \(80^\circ\text{C}\) and \(70^\circ\text{C}\) respectively
4. \(60^\circ\text{C}\) and \(45^\circ\text{C}\) respectively
1. \(89^\circ\text{C}\) and \(73^\circ\text{C}\) respectively
2. \(80^\circ\text{C}\) and \(60^\circ\text{C}\) respectively
3. \(80^\circ\text{C}\) and \(70^\circ\text{C}\) respectively
4. \(60^\circ\text{C}\) and \(45^\circ\text{C}\) respectively
Subtopic: Conduction |
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Level 2: 60%+
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Two cylindrical rods \(A\) and \(B\) made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are: \(\dfrac{L_A}{L_B}=\dfrac{1}{2}, \dfrac{r_A}{r_B}=2\) and \(\dfrac{K_A}{K_B}=\dfrac{1}{2}.\) The free ends of rods \(A\) and \(B\) are maintained at \(400~\text{K}, 200 ~\text{K},\) respectively. The temperature of rods interface is: (in K) when equilibrium is established.
1. \(260\)
2. \(350\)
3. \(366\)
4. \(360\)
1. \(260\)
2. \(350\)
3. \(366\)
4. \(360\)
Subtopic: Conduction |
81%
Level 1: 80%+
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The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have:
| 1. | high thermal conductivity and high electrical conductivity |
| 2. | low thermal conductivity and low electrical conductivity |
| 3. | high thermal conductivity and low electrical conductivity |
| 4. | low thermal conductivity and high electrical conductivity |
Subtopic: Conduction |
Level 4: Below 35%
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Three conductors of same length having thermal conductivity \(k_1, k_2\) and \(k_3\) are connected as shown in figure.
Area of cross sections of \(1^\text{st}\) and \(2^\text{nd}\) conductors are same and for \(3^\text{rd}\) conductor it is double of the \(1^\text{st}\) conductor. The temperatures are given in the figure. In steady state condition, the value of \(\theta\) is:
(Given: \(\mathrm{k}_1=60 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_2=120 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_3=135 \mathrm{~J}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1})\)
1. \(40^\circ \text C\)
2. \(55^\circ \text C\)
3. \(32^\circ \text C\)
4. \(89^\circ \text C\)
| \(100^\circ \text C~~\theta^\circ \text C~~0^\circ \text C\) | |
| 1. \(k_1\) | 3. \(k_3\) |
| 2. \(k_2\) | |
(Given: \(\mathrm{k}_1=60 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_2=120 \mathrm{Js}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1}, \mathrm{k}_3=135 \mathrm{~J}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1})\)
1. \(40^\circ \text C\)
2. \(55^\circ \text C\)
3. \(32^\circ \text C\)
4. \(89^\circ \text C\)
Subtopic: Conduction |
61%
Level 2: 60%+
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The heat passing through the cross-section of a conductor, varies with time \(t\) as \(Q(t)=\alpha t-\beta t^2+\gamma t^3\) (\(\alpha,\beta\) and \(\gamma\) are positive constants). The minimum heat current through the conductor is:
1. \(\alpha-{{\beta^{2}}\over{2\gamma}}\)
2. \(\alpha-{{\beta^{2}}\over{3\gamma}}\)
3. \(\alpha-{{\beta^{2}}\over{\gamma}}\)
4. \(\alpha-{{3\beta^{2}}\over{\gamma}}\)
1. \(\alpha-{{\beta^{2}}\over{2\gamma}}\)
2. \(\alpha-{{\beta^{2}}\over{3\gamma}}\)
3. \(\alpha-{{\beta^{2}}\over{\gamma}}\)
4. \(\alpha-{{3\beta^{2}}\over{\gamma}}\)
Subtopic: Conduction |
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Level 2: 60%+
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Two metallic blocks \(M_1\) and \(M_2\) of the same area of the cross-section are connected to each other (as shown in the figure). If the thermal conductivity of \(M_2\) is \(K,\) then the thermal conductivity of \(M_1\) will be:
(Assume steady state heat conduction)
(Assume steady state heat conduction)
| 1. | \(10K\) | 2. | \(8K\) |
| 3. | \(12.5K\) | 4. | \(2K\) |
Subtopic: Conduction |
83%
Level 1: 80%+
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As per the given figure, two plates \(A\) and \(B\) of thermal conductivity \(K\) and \(2K\) are joined together to form a compound plate. The thickness of the plates are \(4.0~\text{cm}\) and \(2.5~\text{cm}\) respectively and the area of the cross-section is \(120~\text{cm}^2\) for each plate. The equivalent thermal conductivity of the compound plate is \(\left(1+\frac{5}{\alpha}\right) \mathrm{K} \), then the value of \(\alpha\) will be:
1. \(21\)
2. \(10\)
3. \(30\)
4. \(54\)
1. \(21\)
2. \(10\)
3. \(30\)
4. \(54\)
Subtopic: Conduction |
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Level 2: 60%+
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\(K_1\) and \(K_2\) are the thermal conductivities, \(L_1\) and \(L_2\) are the lengths, and \(A_1\) and \(A_2\) are the cross-sectional areas of steel and copper rods respectively such that \(\dfrac{K_{2}}{K_{1}}=9, \dfrac{A_{1}}{A_{2}}=2~\text{and}~ \dfrac{L_{1}}{L_{2}}=2.\) Then, for the arrangement as shown in the figure, the value of the temperature \(T\) of the steel–copper junction in the steady-state will be:
1. \(18^\circ \text{C}\)
2. \(14^\circ \text{C}\)
3. \(45^\circ \text{C}\)
4. \(150^\circ \text{C}\)
1. \(18^\circ \text{C}\)
2. \(14^\circ \text{C}\)
3. \(45^\circ \text{C}\)
4. \(150^\circ \text{C}\)
Subtopic: Conduction |
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Level 1: 80%+
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An ice cube of dimensions 60 cm × 50 cm × 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at 0°C of temperature is brought to a room of temperature 40°C. The rate of melting of ice is approximately:
(Latent heat of fusion of ice is 3.4 × 105 J kg–1 and thermal conducting of insulation wall is 0.05 Wm–1 ºC–1)
1. 61×10–3 kg s–1
2. 61×10–5 kg s–1
3. 208 kg s–1
4. 30×10–5 kg s–1
(Latent heat of fusion of ice is 3.4 × 105 J kg–1 and thermal conducting of insulation wall is 0.05 Wm–1 ºC–1)
1. 61×10–3 kg s–1
2. 61×10–5 kg s–1
3. 208 kg s–1
4. 30×10–5 kg s–1
Subtopic: Conduction |
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Level 2: 60%+
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A rod \({CD}\) with thermal resistance \({10~\text{kW}^{-1}} \) is connected at the midpoint of an identical rod \({AB}.\) The ends \(A, B,\) and \(D\) are maintained at \(200^{\circ} \text{C}, 100^{\circ} \text{C} ,\) and \(125^{\circ} \text{C}\) respectively. The heat current in the rod \(CD\) is:
| 1. | \(4~\text W\) | 2. | \(6~\text W\) |
| 3. | \(2~\text W\) | 4. | \(8~\text W\) |
Subtopic: Conduction |
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Level 2: 60%+
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