Question

3.5 kJ of heat are added to a 3.4 kg block of ice at temperature of -7.6oC. Suppose the amount of heat added to the ice block is doubled. By what factor must the mass of the ice be increased if the system is to have the same final temperature?

Answer 1

In order to have the same final temperature, the mass of the ice must be increased by a factor of 2.

First, we have to obtain the final temperature of the ice;

From;

H = mc(θ2 - θ1)

Where;

m = mass of the ice

c = specific heat capacity of the ice

θ2 = final temperature of the ice

θ1 = Initial temperature of the ice

H = heat added to the ice

Substituting values;

3500 = 3.4 × 2093 × (θ2 - (-7.6))

3500 = 7116.2θ2  +  54083.12

3500 - 54083.12 = 7116.2θ2

θ2 = - 7.1°C

Since the heat added to the ice block is doubled;

H = 2 × 3500 = 7000 J

H = mc(θ2 - θ1)

7000 = m × 2093 × ((- 7.1) - (-7.6))

m = 7000/2093 × ((- 7.1) - (-7.6))

m = 6.8 Kg

The factor by which the mass must be increased in obtained as; 6.8 Kg/3.4 kg

=  2

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