Final answer:
To find the mass of the copper block, we can use the principle of heat transfer. The heat lost by the copper block is equal to the heat gained by the water. Using the given values and solving for the final temperature, we can find that the mass of the copper block is approximately 163.9 g.
Step-by-step explanation:
To find the mass of the copper block, we can use the principle of heat transfer. The heat lost by the copper block is equal to the heat gained by the water.
Qcopper = mcopper * ccopper * ΔTcopper, where mcopper is the mass of the copper block, ccopper is the specific heat of copper, and ΔTcopper is the change in temperature of the copper block.
Qwater = mwater * cwater * ΔTwater, where mwater is the mass of water, cwater is the specific heat of water, and ΔTwater is the change in temperature of the water.
Since the system reaches thermal equilibrium, the heat lost by the copper block is equal to the heat gained by the water: mcopper * ccopper * ΔTcopper = mwater * cwater * ΔTwater.
We can plug in the given values:
mcopper * 0.385 J/g·°C * (65.4 °C - T) = 95.7 g * 4.184 J/g·°C * (T - 22.7 °C)
Now we can solve for T, which will give us the final temperature of the system:
mcopper * 0.385 * 65.4 - mcopper * 0.385 * T = 95.7 * 4.184 * T - 95.7 * 4.184 * 22.7
Simplifying, we have:
mcopper * 25.191 - mcopper * 0.385 * T = 400.320 * T - 904.470
Collecting like terms:
(25.191 + 0.385 * T) * mcopper = 400.320 * T - 904.470
Dividing both sides by (25.191 + 0.385 * T), we get:
mcopper = (400.320 * T - 904.470) / (25.191 + 0.385 * T)
Now we can substitute the final temperature of 24.2 °C to find the mass of the copper block:
mcopper = (400.320 * 24.2 - 904.470) / (25.191 + 0.385 * 24.2)
Simplifying, we find that mcopper is approximately 163.9 g.