Two liquids flow through a heat exchanger and exchange heat energy.
The first liquid has a mass flow rate \(\Big(\dfrac{dm}{dt}\Big)=r_1,\) and its temperature rises by \(\Delta\theta_1.\) For the second liquid, the flow rate \(\Big(\dfrac{dm}{dt}\Big)=r_2,\) and the temperature fall is \(\Delta\theta_2.\) The ratio of their specific heat capacities is:
1.  \(\dfrac{\Delta\theta_1}{\Delta\theta_2}\)
2.  \(\dfrac{r_1}{r_2}\)
3.  \(\dfrac{r_2\Delta\theta_2}{r_1\Delta\theta_1}\)
4.  \(\dfrac{r_2\Delta\theta_1}{r_1\Delta\theta_2}\)

Subtopic:  Calorimetry |
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A body cools from \(52^\circ \text{C}\) to \(48^\circ \text{C}\) in \(6\) minutes. How much time will the same body take to cool from \(53^\circ \text{C}\) to \(47^\circ \text{C}?\) Assume cooling is linear with time.
1. \(12\) minutes
2. \(9\) minutes
3. \(8\) minutes
4. \(7\) minutes
Subtopic:  Newton's Law of Cooling |
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A vessel containing water is heated from the top by means of a heater, just above the water surface. Assume that the temperature of the water was just above \(0^\circ\mathrm{ C},\) in the beginning. The temperature \((\theta_A)\) at the bottom is measured as a function of time. Which of the following shows the correct plot?
                                  
          
1. a
2. b
3. c
4. d
Subtopic:  Convection |
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A body loses heat at a rate of \(2\) W/min when it is at a temperature of \(40^{\circ}\mathrm C,\) but at a rate of \(1\) W/min when its temperature is \(30^{\circ}\mathrm C.\) The temperature of the surroundings is:
1. \(25^{\circ}\mathrm C\)
2. \(20^{\circ}\mathrm C\)
3. \(10^{\circ}\mathrm C\)
4. \(35^{\circ}\mathrm C\)
Subtopic:  Newton's Law of Cooling |
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Ice (\(0^{\circ}\)C) is kept in an insulated reservoir with an opening that is covered at the top with a cloth. When a black cloth \((B)\) is placed at the top, the ice melts at \(2\) g/\(3\) min. When an ordinary cloth \((G)\) is placed, the rate of melting is \(2\) g /\(5\) min. The emissivity of \(G\) is: (assuming that \(B\) behaves as a blackbody)
                       
1. \(0.6\) 2. \(0.3\)
3. \(0.4\) 4. \(0.5\)
Subtopic:  Stefan-Boltzmann Law |
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A radiation blackbody has the shape of a sphere of radius \(r.\) Its surface is at a temperature \(T\) (in Kelvin). If the temperature is doubled and the radius is halved, the total rate of radiation emitted from the body:
1. increases by a factor of \(4\)
2. increases by a factor of \(2\)
3. remains unchanged
4. decreases by a factor of \(2\)
Subtopic:  Stefan-Boltzmann Law |
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\(200\) g of water at \(20^\circ\)C and \(300\) g of water at \(70^\circ\)C are mixed in a calorimeter of negligible heat capacity. Assume no loss of heat. The final temperature is: 
1. \(40^\circ\)C
2. \(50^\circ\)C
3. \(60^\circ\)C
4. \(45^\circ\)C
Subtopic:  Calorimetry |
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Three rods of identical dimensions but made of materials of conductivities \(K,~2K,~K\) are connected in series. The two ends \(A~,B\) are maintained at temperatures of \(0~^{\circ} \text{C},~100~^{\circ} \text{C}\) respectively. Assume no loss of heat from the sides. The temperatures of the junctions \(X,~Y\) are:
                  
1. \(25~^\circ\text C,~75~^\circ\text C\)
2. \(40~^\circ\text C,~60~^\circ\text C\)
3. \(20~^\circ\text C,~80~^\circ\text C\)
4. \(30~^\circ\text C,~70~^\circ\text C\)
Subtopic:  Conduction |
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Mercury having a coefficient of thermal expansion \(\gamma\) is poured into a thin glass tube, which does not expand on heating. The length of the mercury column is \(L.\) If the temperature is raised by \(\theta,\) the new length of the mercury column will be:
1. \(L(1+\gamma\theta)\)
2. \(L(1+\frac\gamma2\theta)\)
3. \(L(1+\frac\gamma3\theta)\)
4. \(L(1+\frac{2\gamma}3\theta)\)
Subtopic:  Thermal Expansion |
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When the temperature difference between a body and its surroundings is \(20\)°C, it loses heat to the surroundings at a rate of \(40\) W. If the temperature difference increases to \(25\)°C, the rate of loss of heat is:
1. \(45\)
2. \(50\) W
3. \(60\)
4. \(80\) W
Subtopic:  Newton's Law of Cooling |
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