If 46.1 g Cu at 11.6 C is placed in 85.0 g H2O at 72.4 C, what is the final temperature of the mixture? (specific heat capacities: Cu: 0.385 J/gK Water: 4.184 J/gK)?
42.0 °C
that answer is wrong
69.50 °C
To find the final temperature of the mixture, we need to use the principle of conservation of heat. The heat lost by the copper (Q1) will be equal to the heat gained by the water (Q2).
The formula to calculate heat is:
Q = mcΔT
Where:
Q - Heat (in joules)
m - Mass (in grams)
c - Specific heat capacity (in J/gK)
ΔT - Change in temperature (in degrees Celsius)
First, let's calculate the heat lost by the copper (Q1):
Q1 = mcΔT
= 46.1 g * 0.385 J/gK * (Tfinal - 11.6 C)
Next, let's calculate the heat gained by the water (Q2):
Q2 = mcΔT
= 85.0 g * 4.184 J/gK * (72.4 C - Tfinal)
Since Q1 = Q2, we can set them equal to each other and solve for the final temperature (Tfinal):
46.1 * 0.385 * (Tfinal - 11.6) = 85.0 * 4.184 * (72.4 - Tfinal)
Now, let's solve this equation for Tfinal:
18Tfinal - 211.66 = 299.976 - 4.184Tfinal
18Tfinal + 4.184Tfinal = 299.976 + 211.66
22.184Tfinal = 511.636
Tfinal = 511.636 / 22.184
Tfinal ≈ 23.08 C
Therefore, the final temperature of the mixture is approximately 23.08 degrees Celsius.