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 find the final temperature of the mixture, we can apply the principle of conservation of energy, specifically the law of heat transfer. According to this law, the heat gained by one substance is equal to the heat lost by another substance during heat transfer.
In this scenario, the heat lost by the water is equal to the heat gained by the ice cube. We can calculate the heat lost by the water using the formula:
Q = mcΔT
Where:
- Q is the heat lost by the water
- m is the mass of the water
- c is the specific heat capacity of water (4.18 J/g°C)
- ΔT is the change in temperature (final temperature - initial temperature) of the water
We can calculate the heat gained by the ice cube using the formula:
Q = mcΔT
Where:
- Q is the heat gained by the ice cube
- m is the mass of the ice cube
- c is the specific heat capacity of ice (2.09 J/g°C)
- ΔT is the change in temperature (final temperature - initial temperature) of the ice cube
Since the ice cube is initially at 0°C, its initial temperature is its final temperature (ΔT = 0). The water is initially at 28°C, and we are trying to find its final temperature.
Since the heat gained by the ice cube is equal to the heat lost by the water, we can set up an equation:
(mcΔT)water = (mcΔT)ice
Using the given information, we can substitute the values into the equation:
(886g)(4.18 J/g°C)(ΔTwater) = (87g)(2.09 J/g°C)(0°C)
Now we can solve for ΔTwater:
(886g)(4.18 J/g°C)(ΔTwater) = 0
ΔTwater = 0 / (886g)(4.18 J/g°C)
Calculating this value will give us the change in temperature of the water, which we can use to find the final temperature of the mixture.