How many grams of a liquid of specific heat 0-2 cal - g - C at a temperature 40- C must be mixed with 100 gm of a liquid of specific heat 0-5 cal - g - C at a temperature 20- C- so that the final temperature of the mixture becomes 32- C - A- 300 gmB- 295 gmC- 375 gmD- 175 gm

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Calorimetry

How many gram...

Question

How many grams of a liquid of specific heat $0.2 {cal/g}^{\circ} C$ at a temperature $40^{\circ} C$ must be mixed with $100 gm$ of a liquid of specific heat $0.5 {cal/g}^{\circ} C$ at a temperature $20^{\circ} C$ , so that the final temperature of the mixture becomes $32^{\circ} C$ ?

175 gm

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300 gm

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295 gm

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375 gm

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Solution

The correct option is D $375 gm$
Given that,
Mass of liquid 2 $(m_{2}) = 100 gm$
Specific heat of liquid 1 $(c_{1}) = 0.2 {cal/g}^{\circ} C$
Specific heat of liquid 2 $(c_{2}) = 0.5 {cal/g}^{\circ} C$
Temperature of liquid 1 $(θ_{1}) = 40^{\circ} C$
Temperature of liquid 2 $(θ_{2}) = 20^{\circ} C$
Let $m_{1}$ be the required mass of liquid 1.

When both the liquids are mixed, heat transfers between them until they reach thermal equilibrium at $θ = 32^{\circ} C$
Using principle of calorimetry, we can say that.
Heat lost by liquid 1 = Heat gained by liquid 2
i.e $m_{1} c_{1} (θ_{1} - θ) = m_{2} c_{2} (θ - θ_{2})$
Thus, temperature of mixture can be written as,
$θ = \frac{m_{1} c_{1} θ_{1} + m_{2} c_{2} θ_{2}}{m_{1} c_{1} + m_{2} c_{2}}$
$\Rightarrow 32 = \frac{m_{1} \times 0.2 \times 40 + 100 \times 0.5 \times 20}{m_{1} \times 0.2 + 100 \times 0.5}$
$\Rightarrow 8 m_{1} + 1000 = 6.4 m_{1} + 1600$
$\Rightarrow 1.6 m_{1} = 600$
$\Rightarrow m_{1} = 375 g$
Thus, option (d) is the correct answer.

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Calorimetry

Standard XII Physics

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How many grams of a liquid of specific heat 0.2 cal/g ∘C at a temperature 40∘C must be mixed with 100 gm of a liquid of specific heat 0.5 cal/g∘C at a temperature 20∘C, so that the final temperature of the mixture becomes 32∘C?

How many grams of a liquid of specific heat $0.2 {cal/g}^{\circ} C$ at a temperature $40^{\circ} C$ must be mixed with $100 gm$ of a liquid of specific heat $0.5 {cal/g}^{\circ} C$ at a temperature $20^{\circ} C$ , so that the final temperature of the mixture becomes $32^{\circ} C$ ?