104 {\g} of water at 30^{\circ} {\C} is taken in a calorimeter made of copper of mass 42 {\g} . When a certain mass of ice at 0^{\circ} {\C} is added to it, the final steady temperature of the mixture after the ice has melted, was found to be 10^{\circ}{\C}. Find the mass of ice added. [Specific heat capacity of water =4.2 {\Jg}^{-1}{ }^{\circ} {\C}^{-1} ; Specific latent heat of fusion of ice =336 {\Jg}^{-1}; Specific heat capacity of copper =0.4 {\Jg}^{-1} { }^{\circ} C^{-1}]

ICSE Class 10 Physics 2019 Solved Paper - Question 67

Question : 67 of 74

Marks: +1, -0

104 {\g}

of water at

30^{∘} {\C}

is taken in a calorimeter made of copper of mass

42 {\g}

. When a certain mass of ice at

0^{∘} {\C}

is added to it, the final steady temperature of the mixture after the ice has melted, was found to be

10^{∘}{\C}

. Find the mass of ice added.
[Specific heat capacity of water

=4.2 {\Jg}^{-1}{ }^{∘} {\C}^{-1}

;
Specific latent heat of fusion of ice

=336 {\Jg}^{-1};

Specific heat capacity of copper

=0.4 {\Jg}^{-1}

{ }^{∘} C^{-1}]

Solution:

Let the mass of ice added be

=

m

' grams
According to the principle of calorimetry,
Heat gained by ice to melt and then convert to water at

10^{∘} {\C}

= Heat lost by water + Heat lost by calorimetry.

m {\L}+m {\C}_{ {\W}} ∆ {\T}\;=m_{ {\W}} × {\C}_{ {\W}} × ∆ {\T}_{ {\w}}+m_{ {\C}}

× {\C}_{ {\C}} × ∆ {\T}_{ {\C}}

m × 336+m\;× 4.2 ×(10-0)

=104 × 4.2 ×(30-10)+42× 0.4 ×(30-10)

336 m+42 m\;=8736+336

378 m\;=9072

m\;=\;{9072}/{378}={2 4 g}

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