(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 1 Thermal Properties of Matter: Thermometry, Expansion and Calorimetry Principle of Calorimetry and Water Equivalent

Difficult

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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1 Thermal Properties of Matter: Thermometry, Expansion and Calorimetry

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Principle of Calorimetry and Water Equivalent

When $x \text{ grams}$ of steam at $100^{\circ}C$ is mixed with $y \text{ grams}$ of ice at $0^{\circ}C$,we obtain $(x + y) \text{ grams}$ of water at $100^{\circ}C$. What is the ratio $y/x$?

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Steam at $100^{\circ} C$ is passed into $1 \ kg$ of water contained in a calorimeter of water equivalent $0.2 \ kg$ at $9^{\circ} C$ until the temperature of the calorimeter and water in it increases to $90^{\circ} C$. The mass of steam condensed in $kg$ is nearly (specific heat of water $= 1 \ cal/g^{\circ} C$, latent heat of vaporisation $= 540 \ cal/g$)

DifficultTS EAMCET 2014

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$2 \ kg$ of ice at $-20^{\circ} C$ is mixed with $5 \ kg$ of water at $20^{\circ} C$. The final mass of water formed is: (in $kg$)

EasyAP EAMCET 2017

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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:

Medium

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Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is held at a temperature of $100^{\circ} C$,while the other one is kept at $0^{\circ} C$. If the two are brought into contact,then assuming no heat loss to the environment,the final temperature that they will reach is

MediumNEET 2016

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When $x \text{ grams}$ of steam at $100^{\circ}C$ is mixed with $y \text{ grams}$ of ice at $0^{\circ}C$,we obtain $(x + y) \text{ grams}$ of water at $100^{\circ}C$. What is the ratio $y/x$?

$2 \ kg$ of ice at $-20^{\circ} C$ is mixed with $5 \ kg$ of water at $20^{\circ} C$. The final mass of water formed is: (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:

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