\(100\) g water at \(20^\circ\text{C}\) is mixed with \(300\) g water at \(100^\circ\text{C}\) in a calorimeter. The mixture is now mixed again with \(400\) g water at \(10^\circ\text{C}.\) The final temperature of the mixture, assuming no loss of heat, is:
1. \(16^\circ\text{C}\)
2. \(30^\circ\text{C}\)
3. \(40^\circ\text{C}\)
4. \(45^\circ\text{C}\)

Subtopic: Ā Calorimetry |
Ā 71%
Level 2: 60%+
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A rod \(\mathrm{A}\) has a coefficient of thermal expansion \((\alpha_A)\) which is twice of that of rod \(\mathrm{B}\) \((\alpha_B)\). The two rods have length \(l_A,~l_B\) where \(l_A=2l_B\). If the two rods were joined end-to-end, the average coefficient of thermal expansion is:

1. \(\alpha_A\) 2. \(\dfrac{2\alpha_A}{6}\)
3. \(\dfrac{4\alpha_A}{6}\) 4. \(\dfrac{5\alpha_A}{6}\)
Subtopic: Ā Thermal Expansion |
Ā 60%
Level 2: 60%+
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The ice-point reading on a thermometer scale is found to be \(20^\circ,\) while the steam point is found to be \(70^\circ.\) When this thermometer reads \(100^\circ ,\) the actual temperature is:
1. \(80^\circ\text{C}\)
2. \(130^\circ\text{C}\)
3. \(160^\circ\text{C}\)
4. \(200^\circ\text{C}\)

Subtopic: Ā Temperature and Heat |
Ā 79%
Level 2: 60%+
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A gas thermometer measures the temperature by measuring the pressure of a constant volume of gas (considered to be ideal). The pressure is directly proportional to the absolute temperature. The pressure at \(27^\circ\text{C}\) is found to be \(15\) kPa. When the pressure is \(20\) kPa, the temperature is:
1. \(20.25^\circ\text{C}\)
2. \(127^\circ\text{C}\)
3. \(225^\circ\text{C}\)
4. \(36^\circ\text{C}\)

Subtopic: Ā Temperature and Heat |
Ā 73%
Level 2: 60%+
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The temperature at which the Celsius and Fahrenheit thermometers agree (to give the same numerical value) is:

1. \(-40^\circ\) 2. \(40^\circ\)
3. \(0^\circ\) 4. \(50^\circ\)
Subtopic: Ā Temperature and Heat |
Ā 86%
Level 1: 80%+
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Two rods of identical dimensions are joined end-to-end, and the ends of the composite rod are kept at \(0^\circ\text{C}\) and \(100^\circ\text{C}\) (as shown in the diagram). The temperature of the joint is found to be \(40^\circ\text{C}.\) Assuming no loss of heat through the sides of the rods, the ratio of the conductivities of the rods \(\dfrac{K_1}{K_2}\) is:

1. \(\dfrac32\) 2. \(\dfrac23\)
3. \(\dfrac11\) 4. \(\dfrac{\sqrt3}{\sqrt2}\)
Subtopic: Ā Conduction |
Ā 80%
Level 1: 80%+
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A piece of alloy of mass \(250~\text{g}\) (specific heat capacity \(=0.1 \times\) that of water) is placed in a furnace and then put into a calorimeter containing \(240~\text{g}\) of water at \(20^\circ\text{C}.\) The water equivalent of the calorimeter is \(10~\text{g}\). The final temperature of the mixture is \(50^\circ\text{C}.\) The temperature of the furnace is (nearly):
1. \(250^\circ\text{C}\) 2. \(350^\circ\text{C}\)
3. \(600^\circ\text{C}\) 4. \(800^\circ\text{C}\)
Subtopic: Ā Calorimetry |
Ā 68%
Level 2: 60%+
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A glass vessel of volume \(V_0\) contains a liquid which fills \(20\%\) of its volume. When the temperature of the system is raised by \(10^\circ\text C,\) the volume of the unfilled portion is found to remain constant. If the coefficient of linear expansion of glass is \(\alpha,\) the coefficient of expansion of the liquid is:
1. \(5 \alpha \) 2. \(\dfrac{3 \alpha}{5} \)
3. \(\dfrac{5 \alpha}{3} \) 4. \(15 \alpha\)
 
Subtopic: Ā Thermal Expansion |
Level 3: 35%-60%
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If the ends of the meter stick are maintained at \(\theta_1\)\(^\circ \text{C}\) and \(\theta_2\)\(^\circ \text{C},\) the temperatures measured at the \(25\) cm and \(80\) cm marks are observed to be \(35^\circ \text{C}\) and \(68^\circ \text{C}\) respectively. Then the temperatures of the left end
(\(\theta_1\)\(^\circ \text{C}\)) and the right end (\(\theta_2\)\(^\circ \text{C}\)) are: 
1. \(\theta_{1}=0, ~\theta_{2}=90\)   
2. \(\theta_{1}=10,~\theta_{2}=85\)
3. \(\theta_{1}=20, ~\theta_{2}=80\)
4. \(\theta_{1}=30, ~\theta_{2}=100\)
Subtopic: Ā Conduction |
Ā 70%
Level 2: 60%+
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When the temperature difference between a body and its surroundings is \(20^{\circ}\text{C}\), it loses heat to the surroundings at a rate of \(40\) W. If the temperature difference increases to \(25^{\circ}\text{C}\), the rate of loss of heat is:
1. \(45\)
2. \(50\) W
3. \(60\)
4. \(80\) W
Subtopic: Ā Newton's Law of Cooling |
Ā 77%
Level 2: 60%+
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