$2 kg$ of water at $100 ° C$ is contained in a vessel of negligible heat capacity. Into this water is added $3 kg$ of ice at $0 ° C$ . Calculate the amount of water at $0 ° C$ at the end of experiment. Take SHC of water $= 4.2 {Jg}^{- 1} {{}^{\circ}C}^{- 1}$ and SLH of ice $= 336 \times 10^{3} J / Kg$ .

Open in App

Solution

Step 1: Given data,
Mass of water, $m = 2 k g a t 100^{\circ} C$
Mass of ice $= 3 k g a t 0^{\circ} C$
SHC of water $= c = 4.2 {Jg}^{- 1} {{}^{\circ}C}^{- 1} = 4200 J K g^{- 1} {{}^{\circ}C}^{- 1}$
SLH of ice $= L = 336 \times 10^{3} J / K g$
Step 2: Finding the heat energy lost by water.
Let us assume that the mass of ice at $0 ° C$ is melted to water at $0 ° C$ .
So the heat energy lost by $2 kg$ of water at $100 ° C$ to cool to $0 ° C$ water,
$= m c (100 - 0) = 100 m c$

Step 3: Finding the heat energy gained by ice.
Heat lost by water = Heat gained by $M$ kg of ice
$100 m c = M L 100 \times 2 \times 4200 = M \times 336000 M = \frac{8400 \times 100}{336000} = 2.5 k g$
Step 4: Finding the amount of water at $0 ° C$
$A m o u n t o f w a t e r a t 0 ° C = 2 kg + 2.5 kg obtained by melting of ice = 4.5 kg$
Hence, the amount of water $a t 0 ° C$ is $4.5 k g$ .

Suggest Corrections

Similar questions

A vessel with a negligible heat capacity contains $1000 g$ ice at $0 ° C$ . Into it is poured $100 g$ of water at $100 ° C$ . What would be the result at the end of experiment ?
[Take SHC of water $= 4.2 {Jg}^{- 1} {{}^{\circ}C}^{- 1}$ and SLH of ice $= 336 {Jg}^{- 1}$ ]

Q. 2 kg of water at 100°c is contained in a vessel of negligible heat capacity. In to this water is added 3 kg of ice at 0°c .Calculate the amount of water at 0 °c at the end of experiment? ( Take sp. heat capacity of water 4.2 ×10 raise to the power 3 J and sp. latent heat of ice 336×10 raise to the power 3 J)

$500 g$ of water at $60 ° C$ is contained in a vessel of negligible heat capacity. Into this water is added $400 g$ of ice at $0 ° C$ . Calculate the amount of ice which does not melt.
[Take $S . H . C$ of water $= 4.2 J g^{- 1} {{}^{\circ}C}^{- 1}$ and $S . L . H$ of ice $= 336 {Jg}^{- 1}$ ]

Q. 500 g of water at 60°c is contained in a vessel of negligible heat capacity. Into this water is added 400 g of ice at 0°c.Calculate the amount of ice which does not melt?( Take S.H.C of water =4.2J/g/°c and sp. latent heat of ice =336 J/g)

Water at $100^{\circ} C$ is poured into a bucket containing $4 K g$ of crushed ice at $0^{\circ} C$ , such that all the ice melts and the final temperature recorded is $0^{\circ} C$ . Calculate the amount of hot water added to the ice. [Take specific heat capacity of water $4200 J K g^{- 1} K^{- 1}$ and specific latent heat of ice $336000 J K g^{- 1}$ .

Join BYJU'S Learning Program

2kg of water at 100°C is contained in a vessel of negligible heat capacity. Into this water is added 3kg of ice at 0°C. Calculate the amount of water at 0°C at the end of experiment. Take SHC of water =4.2Jg-1C∘-1 and SLH of ice =336×103J/Kg.