(D) Let $m$ be the mass of each liquid and $S_A, S_B, S_C$ be their specific heat capacities.For the mixture of $A$ and $B$:$m S_A (15 - 10) = m S_B (

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(D) Let $m$ be the mass of each liquid and $S_A, S_B, S_C$ be their specific heat capacities.For the mixture of $A$ and $B$:$m S_A (15 - 10) = m S_B (25 - 15)$$5 S_A = 10 S_B \Rightarrow S_A = 2 S_B$For the mixture of $B$ and $C$:$m S_B (30 - 25) = m S_C (40 - 30)$$5 S_B = 10 S_C \Rightarrow S_B = 2 S_C \Rightarrow S_C = \frac{S_B}{2}$For the mixture of $A$ and $C$ with final temperature $\theta$:$m S_A (\theta - 10) = m S_C (40 - \theta)$Substitute $S_A = 2 S_B$ and $S_C = \frac{S_B}{2}$:$2 S_B (\theta - 10) = \frac{S_B}{2} (40 - \theta)$$4 (\theta - 10) = 40 - \theta$$4\theta - 40 = 40 - \theta$$5\theta = 80$$\theta = 16^{\circ}C$

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

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Equal masses of three liquids $A, B$ and $C$ have temperatures $10\,^{\circ}C$,$25\,^{\circ}C$ and $40\,^{\circ}C$ respectively. If $A$ and $B$ are mixed,the mixture has a temperature of $15\,^{\circ}C$. If $B$ and $C$ are mixed,the mixture has a temperature of $30\,^{\circ}C$. If $A$ and $C$ are mixed,the mixture will have a temperature of ........ $^{\circ}C$

A
$29$
B
$25$
C
$20$
D
$16$

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10-1.Thermometry, Thermal Expansion and Calorimetry

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Principle of Calorimetry and Water Equivalent

Objects $A$ and $B$ that are initially separated from each other and well isolated from their surroundings are then brought into thermal contact. Initially $T_A = 0^{\circ}C$ and $T_B = 100^{\circ}C$. The specific heat of $A$ is less than the specific heat of $B$. After some time,the system comes to an equilibrium state. The final temperatures are :

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In a calorimeter of water equivalent $20 \,g$,water of mass $1.1 \,kg$ is taken at $288 \,K$ temperature. If steam at temperature $373 \,K$ is passed through it and the temperature of the water increases by $6.5^{\circ} C$,then the mass of steam condensed is ............ $g$.

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$A$ copper block of mass $5.0 \, kg$ is heated to a temperature of $500^{\circ} C$ and is placed on a large ice block. What is the maximum amount of ice (in $kg$) that can melt? [Specific heat of copper: $0.39 \, J g^{-1} {}^{\circ} C^{-1}$ and latent heat of fusion of water: $335 \, J g^{-1}$]

MediumJEE MAIN 2022

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$1\,\,kg$ of ice at $-10^{\circ}C$ is mixed with $4.4\,\,kg$ of water at $30^{\circ}C$. The final temperature of the mixture is $........^{\circ}C$ (specific heat of ice is $2100\,\,J/kg/K$ and latent heat of fusion of ice is $336000\,\,J/kg$)

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An electric kettle (rated at $2.5\, kW$) is used to heat $3\, kg$ of water from $15\, ^oC$ to its boiling point. It takes $9.5$ minutes. The amount of heat lost is:

Medium

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In a calorimeter of water equivalent $20 \,g$,water of mass $1.1 \,kg$ is taken at $288 \,K$ temperature. If steam at temperature $373 \,K$ is passed through it and the temperature of the water increases by $6.5^{\circ} C$,then the mass of steam condensed is ............ $g$.

$A$ copper block of mass $5.0 \, kg$ is heated to a temperature of $500^{\circ} C$ and is placed on a large ice block. What is the maximum amount of ice (in $kg$) that can melt? [Specific heat of copper: $0.39 \, J g^{-1} {}^{\circ} C^{-1}$ and latent heat of fusion of water: $335 \, J g^{-1}$]

$1\,\,kg$ of ice at $-10^{\circ}C$ is mixed with $4.4\,\,kg$ of water at $30^{\circ}C$. The final temperature of the mixture is $........^{\circ}C$ (specific heat of ice is $2100\,\,J/kg/K$ and latent heat of fusion of ice is $336000\,\,J/kg$)

An electric kettle (rated at $2.5\, kW$) is used to heat $3\, kg$ of water from $15\, ^oC$ to its boiling point. It takes $9.5$ minutes. The amount of heat lost is:

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