Question

Suppose you want to cool 0.25 kg of cola (mostly water), at 25°C, by adding ice initially at -20°C. How much ice should you add so that the final temperature will be 0°C with all the ice melt?
Neglect the heat capacity of the container. Specific heat of ice is 2000 J kg K-1.
[Take specific heat of cola 4160 J/kg K]​

Answer 1

[Q]_____?

Heat lost by the cola is

Q (cola) = m (cola) s (cola) ∆T (cola)

=(0. 25kg) (4160 J/kg K) (25°C - 0°C)

= 26, 000 J

Let the mass of the required ice be m (ice) , then the heat needed to warm it from -20°C to 0° is

Q1 = m (ice) s (ice) ∆T (ice)

= m (ice) (2000J kg^-1 K^-1 ) [0°C -(-20°C)]

= m (ice) (4. 0× 10^4 J kg^-1 )

The heat needed to melt this mass of

ice is :

Q2 = m (ice) L (f)

= m (ice) ( 3.34 × 10^5 J kg^-1 )

∴ Total Energy gained by ice is

Q1 + Q2 = m (ice) ( 3. 74 × 10^5 J kg^-1 )

Using Heat lost = Heat gained by ice is

26000 J = m (ice) (3. 74 × 10^5 J kg^-1 )

or,

m (ice) = 0.07 Kg = 70 g

___________________________________

Answer 2

Answer:

m(ice) = 0.07kg= 70g-» answer