A cup of tea contains 175 g of water at a temperature of 85.0 °C. Milk at a temperature of 4.5 °C is added to the tea and the temperature of the mixture becomes 74.0 °C. What is the internal energy lost by the water? What is the mass of the milk?

(a) In a question like this, you will be given that the Specific Heat Capacity of water is 4200Jkg^-1K^-1. However, commiting this to memory will be helpful.

Start with the equation:

E=mC(T₁-T₀)

Find which variables you have and convert to Standard Units:

E=What we want.

m=175g=0.175kg

C=4200Jkg^-1K^-1

T₀=85^oC=358^oK

T₁=74^oC=347^oK

Substitute in and E=0.1754200(347-358)=-8085J or =-8.085kJ   *Negative indicates that the energy is LOST.

(b) Use the equation again and find which variables you know. Convert to Standard Units again.

E=+8085J   The energy LOST by the water must be GAINED by the milk. (Assume none is lost to the surroundings?

m=What we want

C=3900Jkg^-1K^-1 (You will not be expected to know this, it will be given in the question)

(T₁-T₀)=(74+273)-(4.5+273)=69.5^oK

Substitute in:  8085=m390069.5

Rearrange for m => m=8085/(3900*69.5)=0.0298kg (3s.f.)