The final temperature of the mixture is 43.62 °C
To solve the question above, we apply the law of calorimetry
The law of calorimetry: which states that if there is no lost of heat the surrounding, heat lost is equal to heat gained, or it can be stated as heat absorbed by a cold body is equal to heat released by a hot body, provided there is no lost of heat to the surrounding.
The law above is expressed mathematically as
Cm(t₁-t₃) = C'm'(t₃-t₂)............. Equation 1
Using equation 1 to solve the question,
Let: C = specific heat capacity of glass cup, m = mass of glass cup, C' = specific heat capacity of tea, m' = mass of tea, t₁ = initial temperature of tea, t₂ = initial temperature of glass cup, t₃ = final temperature of the mixture.
From the question,
Given: m = 400 g = 0.4 kg, C = 840 J/kg°C, m' = 200g (tea is a liquid made of water and the volume of water in ml is thesame a its mass in gram) = 0.2 kg, C' = 4186 J/kg.°C, t₁ = 90°C, t₂ = 25°C
Substitute these values into equation 1 and solve for t₃
0.4(840)(90-t₃) = 0.2(4186)(t₃-25)
336(90-t₃) = 837.2(t₃-25)
30240-336t₃ = 837.2t₃-20930
collect like terms
837.2t₃+336t₃ = 30240+20930
1173.2t₃ = 51170
t₃ = 51170/1173.2
t₃ = 43.62 °C
Hence, the final temperature of the mixture is 43.62 °C
