How will i answer this calorimetry question?

Question

An aluminum cup of 200g contains 150g of water at 30 degrees how many cubes of ice at -14 degrees C must be added to the cup to lower the temp of water to 10 degrees C if each cube of ice weighs 10g?

Answer 1

The total heat of the system is made of the thermal capacity of the container (aluminum cup) and the content (water). So set up an equation:

Q = m1s1T + m2s2T where m1 and m2 are the masses, s1 and s2 the specific heats and T is the temperature.

By adding ice, you will lower the temperature because the ice melts and gives up its latent heat and the resulting molten water adds to the water and raises to the equilibrium temperature. Let L be the latent heat of ice.

So, Q1 = 200.s1.130 + 150.30 (original heat content) where s1 is the specific heat of aluminum and specific heat of water is taken as 1.


Q2 = 200.s1.10 + (150 + x).10 where x is the quantity of ice added.

Q1 - Q2 = x.s3.14 + x.L + x.10 where s3 is the specific heat of ice, L is the latent heat of melting.

Plug in the values and solve for x.