A 87-g ice cube at 0°C is placed in 886 g of water at 28°C. What is the final temperature of the mixture?
To determine the final temperature of the mixture, you can use the principle of conservation of energy, also known as the law of energy conservation. According to this principle, the total amount of energy in the system remains constant.
To solve this problem, you can use the formula:
m1c1ΔT1 + m2c2ΔT2 = 0
Where:
m1 and m2 are the masses of the substances (ice and water, respectively),
c1 and c2 are the specific heat capacities of the substances (ice and water, respectively),
ΔT1 and ΔT2 are the changes in temperature of the substances.
From the problem statement, we can gather the following data:
m1 (mass of ice) = 87 g
c1 (specific heat capacity of ice) = 2.09 J/g°C
ΔT1 (change in temperature of ice) = T_final - 0°C
m2 (mass of water) = 886 g
c2 (specific heat capacity of water) = 4.18 J/g°C
ΔT2 (change in temperature of water) = T_final - 28°C
Plugging these values into the formula, we get:
(87 g)(2.09 J/g°C)(T_final - 0°C) + (886 g)(4.18 J/g°C)(T_final - 28°C) = 0
Now we can solve for T_final. Let's simplify the equation:
(181.83 J/°C)(T_final) - (181.83 J/°C)(0°C) + (3703.48 J/°C)(T_final) - (3703.48 J/°C)(28°C) = 0
181.83T_final - 0 + 3703.48T_final - 103904.44 = 0
3871.31T_final = 103904.44
T_final = 103904.44 / 3871.31
T_final ≈ 26.86°C
Therefore, the final temperature of the mixture is approximately 26.86°C.