A piece of ice of mass 40 g is dropped into 200 g of water at 50°C. Calculate the final temperature of water after all the ice has melted. Specific heat capacity of water = 4200 J/kg^oC , Specific latent heat of fusion of ice = 336 x 10³ J/kg.

28.33^oC

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38.88^oC

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45.55^oC

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25.33^oC

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Solution

The correct option is A
28.33^oC

Let t be the final temperature.

Then heat Liberated by water = m x c x Δt

= [200 x 10^-3 x 4.2 x 10³ x (50 - t)]

= (42,000 - 840t)

Heat absorbed by ice to change into water at 0^oC = 40 x 10 x 336 x 10³ = 13,440 J.

Heat absorbed by water to change its temperature from 0^oC to t^oC = (40 x 10^-3 x 4.2x 10³ x t) = 168t

Total heat absorbed by water = (13,440 + 168t) J

According to the principle of calorimetry,

Heat given = Heat taken

or 42000 – 840t = 13440 + 168t

or 42000 - 13440 = 168t + 840t

or 1008t = 28560

or t = 28560/1008 = 28.33^oC

Hence, the final temperature of water is 28.33^oC.

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Similar questions

Q. A piece of ice of mass

40 g

is dropped into

200 g

of water at

50^{o} C

. Calculate the final temperature of the water after all the ice has melted. Specific heat capacity of water

= 4200 J k g^{- 1} K^{- 1}

Specific latent heat of fusion of ice

= 336 \times 10^{3} J k g^{- 1}

A vessel of negligible heat capacity contains 40 g of ice in it at 0⁰C. A metal of mass 50 g at 50⁰C is placed into the ice to melt it. The final temperature of the contents of the vessel is 10⁰C. Find the specific capacity of the metal.

(Specific latent heat of fusion of ice = 336 J/g and Specific heat capacity of water = 4.2 J/g⁰C)

Q. A 5g piece of ice at

- 20^{\circ}

C is put into 10g of water at

30^{\circ}

C. Assuming that heat is enchanged only between the ice and the water, find the final temperature of the mixture. Specific heat capacity of ice

= 2100 J k g^{- 1}^{\circ} C^{- 1}

. Specific heat capacity of water

= 4200 J k g^{- 1}^{\circ} C^{- 1}

and latent heat of fusion of ice

3.36 \times 10^{5} J k g^{- 1}

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A piece of ice of mass 40 g is dropped into 200 g of water at 50°C. Calculate the final temperature of water after all the ice has melted. Specific heat capacity of water = 4200 J/kgoC , Specific latent heat of fusion of ice = 336 x 103 J/kg.

A piece of ice of mass 40 g is dropped into 200 g of water at 50°C. Calculate the final temperature of water after all the ice has melted. Specific heat capacity of water = 4200 J/kg^oC , Specific latent heat of fusion of ice = 336 x 10³ J/kg.