Final answer:
To find the final temperature when a piece of copper is dropped into water, use the principle of heat transfer. The equation Q = mcΔT can be used to equate the heat gained by the water and the heat lost by the copper. By plugging in the known values and solving the equation, the final temperature can be determined to be approximately 50.13 °C.
Step-by-step explanation:
To find the final temperature when a piece of copper is dropped into water, we can use the principle of heat transfer. The heat gained by the water will be equal to the heat lost by the copper. The equation for heat transfer is Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Using the given values, we can solve for the final temperature. The mass of the copper is 248 g and its initial temperature is 314 °C. The mass of the water is 390 g and its initial temperature is 22.6 °C. The specific heat capacity of water is 4.18 J/g°C. Plugging in these values into the equation, we get:
Qcopper = Qwater
mcopperccopper(ΔTcopper) = mwatercwater(ΔTwater)
(248 g)(0.39 J/g°C)(final temperature - 314 °C) = (390 g)(4.18 J/g°C)(final temperature - 22.6 °C)
Expanding and rearranging the equation, we can solve for the final temperature:
84472 - 313.92(final temperature) = 1630.2(final temperature) - 7380.12
Combining like terms, we get:
1644.12(final temperature) = 82492.12
Dividing both sides of the equation by 1644.12, we find that the final temperature is approximately 50.13 °C.