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Q. No.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. \(360\)
Subtopic: Conduction |
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Consider a rectangular sheet of solid material of length \(l = 9 \text{ cm} \) and width \(d = 4 ~\text{cm.} \) The coefficient of linear expansion is \(\alpha = 3.1 \times 10^{-5} ~\text{K} ^{-1}\) at room temperature and one atmospheric pressure. The mass of sheet \( m = 0.1~\text{kg} \) and the specific heat capacity \(C_v = 900 ~\text{Jkg}^{-1}~ \text{K}^{-1} .\) If the amount of heat supplied to the material is \(8.1 × 10^2 ~\text{J}\) then change in area of the rectangular sheet is: (in \(\text{m}^2\))
1. \(6.0\times10^{-7}\)
2. \(4.0\times10^{-7}\)
3. \(2.0\times10^{-6}\)
4. \(3.0\times10^{-7}\)
1. \(6.0\times10^{-7}\)
2. \(4.0\times10^{-7}\)
3. \(2.0\times10^{-6}\)
4. \(3.0\times10^{-7}\)
Subtopic: Thermal Expansion |
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A wire of length \(10~\text{cm} \) and diameter \(0.5 \text{ mm} \) is used in a bulb. The temperature of the wire is \(1727^{\circ} \text{C}\) and power radiated by the wire \(94.2~\text{W}.\) Its emissivity is \(\dfrac{x}{8}\) then the value of \(x\) is:
(Given \(\sigma=6.0 \times 10^{-8}~ {\text{Wm}}^{-2} {~\text K}^{-4} , \pi=3.14 \) and assume that the emissivity of wire material is same at all)
1. \(5 \)
2. \(4\)
3. \(6\)
4. \(7\)
(Given \(\sigma=6.0 \times 10^{-8}~ {\text{Wm}}^{-2} {~\text K}^{-4} , \pi=3.14 \) and assume that the emissivity of wire material is same at all)
1. \(5 \)
2. \(4\)
3. \(6\)
4. \(7\)
Subtopic: Radiation |
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Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Temperature and Heat |
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The temperature of a body in air falls from \(40^\circ \text {C}\) to \(24^\circ \text {C}\) in \(4\) minutes. The temperature of the air is \(16^\circ \text {C}\). The temperature of the body in the next \(4\) minutes will be -
1. \(\dfrac {28}{3}^\circ \text {C}\)
2. \(\dfrac {42}{3}^\circ \text {C}\)
3. \(\dfrac {14}{3}^\circ \text {C}\)
4. \(\dfrac {56}{3}^\circ \text {C}\)
1. \(\dfrac {28}{3}^\circ \text {C}\)
2. \(\dfrac {42}{3}^\circ \text {C}\)
3. \(\dfrac {14}{3}^\circ \text {C}\)
4. \(\dfrac {56}{3}^\circ \text {C}\)
Subtopic: Newton's Law of Cooling |
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A cup of coffee cools from \(90^{\circ} \text{C}\) to \(80^{\circ} \text{C}\) in \(t\) minutes when the room temperature is \(20^{\circ} \text{C}.\) The time taken by the similar cup of coffee to cool from \(80^{\circ} \text{C} \) to \(60^{\circ} \text{C} \) at the same room temperature is:
1. \(\dfrac{13}{10} t\)
2. \(\dfrac{10}{13} t\)
3. \(\dfrac{5}{13} t\)
4. \(\dfrac{13}{5} t\)
1. \(\dfrac{13}{10} t\)
2. \(\dfrac{10}{13} t\)
3. \(\dfrac{5}{13} t\)
4. \(\dfrac{13}{5} t\)
Subtopic: Newton's Law of Cooling |
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A gun fires a lead bullet of temperature \(300~\text K\) into a wooden block. The bullet having melting temperature of \(600~\text K\) penetrates into the block and melts down. if the total heat required for the process is \(625~\text J,\) then the mass of the bullet is grams.
(Latent heat of fusion of lead = \(2.5 × 104 ~\text { JKg}^{-1}\) and specific heat capacity of lead = \(125 \text { JKg}^{-1} \text {K}^{-1} )\)
1. \(15\)
2. \(10\)
3. \(5\)
4. \(20\)
(Latent heat of fusion of lead = \(2.5 × 104 ~\text { JKg}^{-1}\) and specific heat capacity of lead = \(125 \text { JKg}^{-1} \text {K}^{-1} )\)
1. \(15\)
2. \(10\)
3. \(5\)
4. \(20\)
Subtopic: Calorimetry |
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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 |
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Level 3: 35%-60%
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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 |
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An amount of ice of mass \(10^{-3}~ \text {kg}\) and temperature \(10^\circ C\) is transformed to vapour of temperature \(110^ \circ C \) by applying heat. The total amount of work required for this conversion is,
(Take specific heat of ice = \(2100~ \text {JKg}^{-1} \text K^{-1}\)), specific heat of water = \(4180~ \text {JKg}^{-1} \text K^{-1}\), specific heat of steam = \(1920~ \text {JKg}^{-1} \text K^{-1}\),
Latent heat of ice = \(2.25\times 10^5~ \text {JKg}^{-1}\) and Latent heat of steam \(2.25 \times 10^6~ \text {JKg}^{-1}\))
1.\(3043~ \text J\)
2. \(3003~ \text J\)
3. \(3022~ \text J\)
4. \(3024~ \text J\)
(Take specific heat of ice = \(2100~ \text {JKg}^{-1} \text K^{-1}\)), specific heat of water = \(4180~ \text {JKg}^{-1} \text K^{-1}\), specific heat of steam = \(1920~ \text {JKg}^{-1} \text K^{-1}\),
Latent heat of ice = \(2.25\times 10^5~ \text {JKg}^{-1}\) and Latent heat of steam \(2.25 \times 10^6~ \text {JKg}^{-1}\))
1.\(3043~ \text J\)
2. \(3003~ \text J\)
3. \(3022~ \text J\)
4. \(3024~ \text J\)
Subtopic: Calorimetry |
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