Question

Ice at –20° C is added to 50 g of water at 40°C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still not melted. The amount of ice added to the water was close to

(Specific heat of water = 4.2 J/g/°C)

Specific heat of Ice = 2.1 J/g/°C

The heat of fusion of water at 0°C = 334 J/g)

• A. 50 g
• B. 40 g
• C. 60 g
• D. 100 g

Answer 1

The correct option is B

40 g

Given:

Mass of water, ${\mathrm{m}}_{\mathrm{w}}=50\mathrm{g}$

The initial temperature of the water, $T_w={40}^{\circ }C$

The initial temperature of ice, $T_i=-{20}^{\circ }C$

Specific heat of water, $S_w=4.2J/g{/}^{\circ }C$

Specific heat of ice, $S_i=2.1J/g{/}^{\circ }C$

The heat of fusion of water at $0^{\circ }C=H_f=334J/g$

Principle of Calorimetry: At higher temperatures, the body releases heat while at lower temperatures the body absorbs heat. y

• The principle of calorimetry states the law of conservation of energy.
• According to this, the total heat given by the hot body is equal to the total heat received by the cold body.

Let, the amount of ice is $\mathrm{m}\mathrm{gm}.$

Since the final temperature of the whole system is $0^{\circ }C$ , the value of temperature difference for water can be given as:

$$\begin{gathered} {\mathrm{\Delta T}}_{\mathrm{w}}={\mathrm{T}}_{\mathrm{w}}-0^{\circ }\mathrm{C} \\ {\mathrm{\Delta T}}_{\mathrm{w}}={40}^{\circ }\mathrm{C}-0^{\circ }\mathrm{C} \\ {\mathrm{\Delta T}}_{\mathrm{w}}={40}^{\circ }\mathrm{C} \end{gathered}$$

According to the principal of the calorimeter,

The heat is taken by ice = Heat given by water

$$\begin{gathered} \Rightarrow {\mathrm{S}}_{\mathrm{i}}\times \mathrm{m}\times {\mathrm{\Delta T}}_{\mathrm{i}}+{\mathrm{H}}_{\mathrm{f}}(\mathrm{m}-20)={\mathrm{S}}_{\mathrm{w}}\times {\mathrm{m}}_{\mathrm{w}}\times {\mathrm{\Delta T}}_{\mathrm{w}} \\ \Rightarrow 2.1\times 20\times \mathrm{m}+334(\mathrm{m}-20)=4.2\times 50\times 40 \\ \Rightarrow 376\mathrm{m}-6680=8400 \\ \Rightarrow 376\mathrm{m}=15080 \\ \Rightarrow \mathrm{m}=40.1\mathrm{g}\approx 40g \end{gathered}$$

Hence, option B is the correct answer.