the heat capacity of copper is 0.382J/g degrees celsius. a 22.6g sample of copper at 93 degrees celsius is placed in 50g of water at 23.9 degrees celsius. what is the final temperature of the system?
To find the final temperature of the system after the copper and water have reached thermal equilibrium, you can use the principle of heat transfer:
Q(copper) + Q(water) = 0
The heat gained by copper will be equal to the heat lost by water.
The formula to calculate heat transfer is:
Q = mcΔT
where:
Q is the heat transfer
m is the mass of the substance
c is the specific heat capacity
ΔT is the change in temperature
Let's calculate the heat transfer for both copper and water:
For the copper:
Q(copper) = mcΔT(copper)
= (22.6g) × (0.382J/g°C) × (final temperature - 93°C)
For the water:
Q(water) = mcΔT(water)
= (50g) × (4.18J/g°C) × (final temperature - 23.9°C)
Since Q(copper) = -Q(water) (negative because heat is lost for copper and gained for water), we can equate the two equations and solve for the final temperature:
(22.6g) × (0.382J/g°C) × (final temperature - 93°C) = -(50g) × (4.18J/g°C) × (final temperature - 23.9°C)
Now, let's solve this equation step by step:
(8.6336J/°C) × (final temperature - 93) = -(209J/°C) × (final temperature - 23.9)
8.6336(final temperature) - 805.1088 = -209(final temperature) + 4951.1
8.6336(final temperature) + 209(final temperature) = 4951.1 + 805.1088
217.6336(final temperature) = 5756.2088
final temperature = 5756.2088 / 217.6336
final temperature ≈ 26.46°C
Therefore, the final temperature of the system, after thermal equilibrium, is approximately 26.46°C.