(A) The heat required to raise the temperature of the water is given by $Q = mc \Delta \theta$.Here,mass $m = 2 \, kg$ (since density of water is $1 \

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(A) The heat required to raise the temperature of the water is given by $Q = mc \Delta \theta$.Here,mass $m = 2 \, kg$ (since density of water is $1 \, kg/L$),$c = 4.2 \times 10^3 \, J/(kg \cdot K)$,and $\Delta \theta = 77 - 27 = 50 \, ^\circ C$.So,$Q = 2 \times 4.2 \times 10^3 \times 50 = 4.2 \times 10^5 \, J$.The net power supplied to the water is $P_{net} = P_{coil} - P_{loss} = 1000 \, W - 160 \, W = 840 \, W$.The time taken $t$ is given by $t = Q / P_{net}$.$t = (4.2 \times 10^5) / 840 = 500 \, s$.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

Medium

Water of volume $2 \, L$ in a container is heated with a coil of $1 \, kW$ at $27 \, ^\circ C$. The lid of the container is open and energy dissipates at a rate of $160 \, J/s$. In how much time will the temperature rise from $27 \, ^\circ C$ to $77 \, ^\circ C$? [Given: specific heat of water is $4.2 \, kJ/(kg \cdot K)$]

IIT 2004 All IIT

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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Steam at $100^{\circ} C$ is passed into $114 \ g$ of water at $30^{\circ} C$. The mass of water present in the mixture when the temperature of the mixture becomes $70^{\circ} C$ is (Latent heat of steam $= 540 \ cal \ g^{-1}$; specific heat capacity of water $= 1 \ cal \ g^{-1} {}^{\circ} C^{-1}$) (in $g$)

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Steam is passed into $22 \, g$ of water at $20^{\circ}C$. The mass of water that will be present when the water acquires a temperature of $90^{\circ}C$ is ........ $g$. (Latent heat of steam is $540 \, cal/g$)

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When $0.4 \ kg$ of water at $30^{\circ} C$ is mixed with $0.15 \ kg$ of water at $25^{\circ} C$ in a calorimeter,the final temperature is found to be $27^{\circ} C$. Find the water equivalent of the calorimeter. (in $kg$)

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$A$ liquid of mass $m$ and specific heat $c$ is heated to a temperature $2T$. Another liquid of mass $m/2$ and specific heat $2c$ is heated to a temperature $T$. If these two liquids are mixed, the resulting temperature of the mixture is:

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Of two masses of $5 \, kg$ each falling from a height of $10 \, m$,by which $2 \, kg$ of water is stirred. The rise in temperature of the water will be ........ $^\circ C$.

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Steam is passed into $22 \, g$ of water at $20^{\circ}C$. The mass of water that will be present when the water acquires a temperature of $90^{\circ}C$ is ........ $g$. (Latent heat of steam is $540 \, cal/g$)

When $0.4 \ kg$ of water at $30^{\circ} C$ is mixed with $0.15 \ kg$ of water at $25^{\circ} C$ in a calorimeter,the final temperature is found to be $27^{\circ} C$. Find the water equivalent of the calorimeter. (in $kg$)

$A$ liquid of mass $m$ and specific heat $c$ is heated to a temperature $2T$. Another liquid of mass $m/2$ and specific heat $2c$ is heated to a temperature $T$. If these two liquids are mixed, the resulting temperature of the mixture is:

Of two masses of $5 \, kg$ each falling from a height of $10 \, m$,by which $2 \, kg$ of water is stirred. The rise in temperature of the water will be ........ $^\circ C$.

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