(A) Given:Volume of water $V = 2\, L$,so mass $m = 2\, kg$ (since density of water is $1\, kg/L$).Power of coil $P_{in} = 1000\, J/s$.Rate of heat los

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(A) Given:Volume of water $V = 2\, L$,so mass $m = 2\, kg$ (since density of water is $1\, kg/L$).Power of coil $P_{in} = 1000\, J/s$.Rate of heat loss $P_{out} = 160\, J/s$.Temperature change $\Delta T = 77\, ^\circ C - 27\, ^\circ C = 50\, ^\circ C$.Specific heat capacity of water $c = 4.2\, kJ/kg\cdot K = 4200\, J/kg\cdot K$.Net power supplied to the water $P_{net} = P_{in} - P_{out} = 1000\, J/s - 160\, J/s = 840\, J/s$.Total heat required $Q = m \cdot c \cdot \Delta T = 2\, kg \times 4200\, J/kg\cdot K \times 50\, K = 420,000\, J$.Time required $t = \frac{Q}{P_{net}} = \frac{420,000\, J}{840\, J/s} = 500\, s$.Converting to minutes: $500\, s = 8\, min\, 20\, s$.

Class 11 Physics 10-1.Thermometry, Thermal Expansion and Calorimetry Principle of Calorimetry and Water Equivalent

Difficult

Water of volume $2\, L$ in a closed container is heated with a coil of $1\, kW$. While water is heated,the container loses energy at a rate of $160\, J/s$. In how much time will the temperature of water rise from $27\, ^\circ C$ to $77\, ^\circ C$? (Specific heat of water is $4.2\, kJ/kg\cdot K$ and that of the container is negligible)

JEE MAIN 2014 All JEE MAIN

A
$8\, min\, 20\, s$
B
$6\, min\, 2\, s$
C
$7\, min$
D
$14\, min$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Principle of Calorimetry and Water Equivalent

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Some steam at $100^o \, C$ is passed into $1.1 \, kg$ of water contained in a calorimeter of water equivalent $0.02 \, kg$ at $15^o C$ so that the temperature of the calorimeter and its contents rises to $80^o \, C$. What is the mass of steam condensing (in $kg$)?

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We have half a bucket $(6 \text{ litre})$ of water at $20^{\circ}C$. If we want water at $40^{\circ}C$,how much steam at $100^{\circ}C$ should be added to it?

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Two liquids $A$ and $B$ are at temperatures of $75^{\circ} C$ and $15^{\circ} C$. Their masses are in the ratio of $2: 3$ and their specific heats in the ratio $3: 4$. If these two liquids are mixed,then the resulting temperature will be $...^{\circ} C$.

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Two identical blocks of metal are at $20^{\circ} C$ and $80^{\circ} C$,respectively. The specific heat of the material of the two blocks increases with temperature. Which of the following is true about the final temperature $T_f$ when the two blocks are brought into contact (assuming that no heat is lost to the surroundings)?

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The temperature of a copper piece of mass $50 \ g$ is raised by $10 \ ^\circ C$. If the same amount of heat is given to $10 \ g$ of water,the rise in its temperature is = ...... $^\circ C$ (Specific heat of copper $= 420 \ J/kg \cdot ^\circ C$,Specific heat of water $= 4200 \ J/kg \cdot ^\circ C$).

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Some steam at $100^o \, C$ is passed into $1.1 \, kg$ of water contained in a calorimeter of water equivalent $0.02 \, kg$ at $15^o C$ so that the temperature of the calorimeter and its contents rises to $80^o \, C$. What is the mass of steam condensing (in $kg$)?

We have half a bucket $(6 \text{ litre})$ of water at $20^{\circ}C$. If we want water at $40^{\circ}C$,how much steam at $100^{\circ}C$ should be added to it?

Two liquids $A$ and $B$ are at temperatures of $75^{\circ} C$ and $15^{\circ} C$. Their masses are in the ratio of $2: 3$ and their specific heats in the ratio $3: 4$. If these two liquids are mixed,then the resulting temperature will be $...^{\circ} C$.

The temperature of a copper piece of mass $50 \ g$ is raised by $10 \ ^\circ C$. If the same amount of heat is given to $10 \ g$ of water,the rise in its temperature is = ...... $^\circ C$ (Specific heat of copper $= 420 \ J/kg \cdot ^\circ C$,Specific heat of water $= 4200 \ J/kg \cdot ^\circ C$).

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