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

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Solution

Mass of ice $(m_{1}) = 40 g = \frac{40}{1000} k g$
Mass of water $(m_{2}) = 200 g = \frac{200}{1000} k g$
Temperature of water $50^{o} C$ . Let final temp. $= T^{o} C$
Heat taken by ice = Heat given by water
$m_{1} L + m_{1} S_{1} T_{1} = m_{2} S_{2} T_{2}$

$\Rightarrow \frac{40}{1000} \times 336 \times 10^{3} + \frac{40}{1000} \times 4.2 \times 10^{3} \times T$ $= \frac{200}{1000} \times 4.2 \times 10^{3} \times (50 - T)$

$\Rightarrow 40 \times 336 + 40 \times 4.2 T = 200 \times 4.2 \times (50 - T)$

$\Rightarrow 336 + 4.2 T = 21 (50 - T)$
$\Rightarrow 25.2 T = 714 \Rightarrow T = \frac{714}{25.2} = {28.33}^{o} C$

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Similar questions

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.

40 g

of ice at

0^{o} C

is used to bring down the temperature of certain mass of water at

60^{o} C t o 10^{o} C

. Find the mass of water used.
[Specific heat capacity of water

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

[Specific latent heat of fusion of ice

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

]

2 k g

of ice melts when water at

100^{o} C

is poured in a hole drilled in a block of ice. What mass of water was used?

Given: specific heat capacity of water

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

specific latent heat of ice

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

250 g

of water at

30^{o} C

is contained in a copper vessel of mass

50 g

. Calculate the mass of ice required to bring down the temperature of the vessel and its contents to

5^{o} C

. Given : specific latent heat of fusion of ice

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

, specific heat capacity of copper

= 400 J k g^{- 1} K^{- 1}

, specific heat capacity of water

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

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A piece of ice of mass 40 g is dropped into 200 g of water at 50oC. Calculate the final temperature of the water after all the ice has melted. Specific heat capacity of water =4200J kg−1 K−1 Specific latent heat of fusion of ice =336×103 J kg−1

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