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Q. No.The temperature of a metal strip having coefficient of linear expression \(\alpha\) is increased from \(T_1\) to \(T_2\) resulting in increase of its length by \(\Delta{L_1}.\) The temperature is further increased from \(T_2\) to \(T_3\) such that the increase in its length is \(\Delta{L}_2.\)
Given \(T_3+T_1 =2T_2\) and \(T_2-T_1=\Delta{T},\) the value of \(\Delta{L}_2\) is:
1. \(\Delta{L_1}[1+ 2\alpha^{2}(\Delta{T})^{2}]\)
2. \(\Delta{L_1}[1+ \alpha^{2}(\Delta{T})^{2}]\)
3. \(\Delta{L_1}[1+ 2\alpha\Delta{T}^{2}]\)
4. \(\Delta{L_1}[1+ \alpha\Delta{T}]\)
Given \(T_3+T_1 =2T_2\) and \(T_2-T_1=\Delta{T},\) the value of \(\Delta{L}_2\) is:
1. \(\Delta{L_1}[1+ 2\alpha^{2}(\Delta{T})^{2}]\)
2. \(\Delta{L_1}[1+ \alpha^{2}(\Delta{T})^{2}]\)
3. \(\Delta{L_1}[1+ 2\alpha\Delta{T}^{2}]\)
4. \(\Delta{L_1}[1+ \alpha\Delta{T}]\)
Subtopic: Thermal Expansion |
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Level 2: 60%+
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A gas based geyser heats water flowing at the rate of \(5.0\) litres per minute from \(27^{\circ}\text{C}\) to \(87^{\circ}\text{C}\).
The rate of consumption of the gas is:
(Take heat of combustion of gas = \(5.0\times 10^{4}~\text{J/g}\), specific heat capacity of water = \(4200~\text{J/kg}^{\circ}\text{C}\))
1. \(2.1\)
2. \(4.2\)
3. \(0.42\)
4. \(0.21\)
The rate of consumption of the gas is:
(Take heat of combustion of gas = \(5.0\times 10^{4}~\text{J/g}\), specific heat capacity of water = \(4200~\text{J/kg}^{\circ}\text{C}\))
1. \(2.1\)
2. \(4.2\)
3. \(0.42\)
4. \(0.21\)
Subtopic: Calorimetry |
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Level 2: 60%+
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An aluminium and steel rods having same lengths and cross-sections are joined to make total length of \(120~\text{cm}\) at \(30^{\circ}\text{C}\). The coefficient of linear expansion of aluminium and steel are \(24 \times 10^{-6} /{ }^{\circ} \text{C}\) and \(1.2 \times 10^{-5} /{ }^{\circ} \text{C},\) respectively. The length of this composite rod when its temperature is raised to \(100^{\circ}\text{C}\), is: (in cm)
1. \(120.20\)
2. \(120.15\)
3. \(120.03\)
4. \(120.06\)
1. \(120.20\)
2. \(120.15\)
3. \(120.03\)
4. \(120.06\)
Subtopic: Thermal Expansion |
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Level 3: 35%-60%
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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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Density of water at \(4^\circ\text C\) and \(20^\circ\text C\) are \(1000 ~\text{kg/m}^3\) and respectively. The increase energy of \(4~\text{kg}\) water when it is heated from \(4^\circ\text C\) to \(20^\circ\text C\) is: (in J)
(Specific heat capacity of water \(=4.2 ~\text{J/kg}.\) and \(1\) atmospheric pressure \(= 10^5~\text{Pa}\))
1. \(315826.2\)
2. \(234699.2\)
3. \(258700.8\)
4. \(268799.2\)
(Specific heat capacity of water \(=4.2 ~\text{J/kg}.\) and \(1\) atmospheric pressure \(= 10^5~\text{Pa}\))
1. \(315826.2\)
2. \(234699.2\)
3. \(258700.8\)
4. \(268799.2\)
Subtopic: Calorimetry |
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Level 3: 35%-60%
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A brass wire of length \(2~\text m\) and radius \(1~\text{mm}\) at \(27^\circ \text{C}\) is held taut between two rigid supports. Initially it was cooled to a temperature of \(–43^\circ \text{C}\) creating a tension \(T\) in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to \(1.4T,\) is: (in \(^\circ \text{C}\))
1. \(-86\)
2. \(-71\)
3. \(-65\)
4. \(-80\)
1. \(-86\)
2. \(-71\)
3. \(-65\)
4. \(-80\)
Subtopic: Thermal Expansion |
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Level 2: 60%+
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\(10~\text{kg}\) of ice at \(-10^\circ \text{C}\) is added to \(100~\text{kg}\) of water to lower its temperature from \(25^\circ \text {C}\). Consider no heat exchange to surroundings. The decrement to the temperature of water is: (in \(^\circ \text {C}\)) (Specific heat of ice = \(2100~\text{J/kg}^\circ\text{C}\) specific heat of water = \(4200~\text{J/kg}^\circ\text{C}\), latent heat of fusion of ice = \(3.36 \times 10^5 ~\text{J/Kg}\))
1. \(10\)
2. \(15\)
3. \(6.67\)
4. \(11.6\)
1. \(10\)
2. \(15\)
3. \(6.67\)
4. \(11.6\)
Subtopic: Calorimetry |
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Level 3: 35%-60%
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Which of the following best represents the temperature versus heat supplied graph for water, in the range of \(-20^\circ \text C\) to \(120^\circ\text C\)?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Calorimetry |
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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 |
Level 4: Below 35%
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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 |
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Level 1: 80%+
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