Question

If 35.0 g of H₂O at 22.7 °C is combined with 65.0 g of H₂O at 87.5 °C, what is the final temperature of the mixture? The specific heat capacity of water is 4.184 J/g⋅K.

a. 25.1 °C
b. 45.4 °C
c. 50.8 °C
d. 64.8 °C
e. 48.9 °C

Answer 1

To determine the final temperature of a mixture of two water samples, we apply the conservation of energy, using the formula q = mcΔT. The heat lost by the hot water equals the heat gained by the cold water, leading to an equation that can be solved for the final temperature of the water mixture.

Step-by-step explanation:

The question is asking to determine the final temperature of a mixture of two water samples with different initial temperatures. According to the principle of conservation of energy, the heat lost by the hotter water will be equal to the heat gained by the cooler water. The formula used to calculate this is q = mcΔT, where q is the heat exchanged, m is the mass, c is the specific heat capacity, and ΔT is the temperature change.

To find the final temperature (Tfinal), we set the heat lost by the hot water equal to the heat gained by the cold water, which leads to the equation: mhotc(Tinitial,hot - Tfinal) = mcoldc(Tfinal - Tinitial,cold). Since the specific heat c is the same for both, it cancels out. Plugging in the given values and solving for Tfinal gives us the final temperature of the mixture.