Question

"A 47.0 g sample of a metal with a specific heat capacity of 0.830 J/gC and temperature of 40.5 C is placed into 48.9 g of water at a temperature of 80.0 C. What is the final temperature of the mixture?"

Answer 1

The final temperature of the mixture is approximately 58.3°C. In order to find the final temperature of the mixture, we can use the principle of heat transfer and the specific heat formula.

Step-by-step explanation:

In order to determine the final temperature of the mixture, the principle of heat transfer is applied, wherein the heat lost by the metal equals the heat gained by the water.

Utilizing the specific heat formula, the heat lost by the metal (Q) is calculated as (47.0 g)(0.830 J/g°C)(40.5°C - x), where 'x' denotes the final temperature of the mixture.

Simultaneously, the heat gained by the water is determined through the formula (48.9 g)(4.18 J/g°C)(x - 80.0°C).

Setting the two heat expressions equal to each other, we obtain the equation (47.0 g)(0.830 J/g°C)(40.5°C - x) = (48.9 g)(4.18 J/g°C)(x - 80.0°C).

Solving for 'x' in this equation yields a final temperature of approximately 58.3°C.

Therefore, the final temperature of the mixture is approximately 58.3°C.