Q. No.\(100\) 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. \(45^\circ\text{C}\)
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. | \(\dfrac{5\alpha_A}{6}\) |
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. \(200^\circ\text{C}\)
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. \(36^\circ\text{C}\)
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. | \(50^\circ\) |
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. | \(\dfrac{\sqrt3}{\sqrt2}\) |
| 1. | \(250^\circ\text{C}\) | 2. | \(350^\circ\text{C}\) |
| 3. | \(600^\circ\text{C}\) | 4. | \(800^\circ\text{C}\) |
| 1. | \(5 \alpha \) | 2. | \(\dfrac{3 \alpha}{5} \) |
| 3. | \(\dfrac{5 \alpha}{3} \) | 4. | \(15 \alpha\) |
(\(\theta_1\)\(^\circ \text{C}\)) 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. | \(\theta_{1}=30, ~\theta_{2}=100\) |
1. \(45\) W
2. \(50\) W
3. \(60\) W
4. \(80\) W
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