Question

A student mixes 81 g of liquid water at a temperature of 23°C with 55 g of liquid water at a temperature of 56°C. What is the final temperature of the combined mix?

a) 29.31°C
b) 34.53°C
c) 39.44°C
d) 43.76°C

Answer 1

To find the final temperature of the combined mix, we can use the principle of heat transfer and the formula Q = m * c * ΔT. By setting the heat gained by the colder water equal to the heat lost by the hotter water and solving the resulting equation, we find the final temperature to be approximately 34.53°C.

Step-by-step explanation:

To find the final temperature of the combined mix, we can use the principle of heat transfer, which states that the heat gained by the colder water is equal to the heat lost by the hotter water. We can calculate the heat gained/lost using the formula Q = m * c * ΔT, where Q is the heat gained/lost, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.

For the colder water:
Qcolder = m * c * ΔTcolder = 81 g * 4.18 J/g°C * (Final Temperature - 23°C)

For the hotter water:
Q = m * c * ΔT = 55 g * 4.18 J/g°C * (56°C - Final Temperature)

Since the heat gained by the colder water is equal to the heat lost by the hotter water, we can set these two formulas equal to each other and solve for the Final Temperature:

81 g * 4.18 J/g°C * (Final Temperature - 23°C) = 55 g * 4.18 J/g°C * (56°C - Final Temperature)

Solving this equation, we find the Final Temperature to be approximately 34.53°C.