# $$200$$ 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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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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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 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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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 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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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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The density of water at $$20^\circ \text{C}$$ is $$998$$ kg/m3 and at $$40^\circ \text{C}$$ is $$992$$ kg/m3. The coefficient of volume expansion of water is:
1. $$3 \times 10^{-4} / ^\circ\text C$$
2. $$2 \times 10^{-4} / ^\circ\text C$$
3. $$6 \times 10^{-4} / ^\circ\text C$$
4. $$10^{-4} / ^\circ\text C$$