You drop 378 g of solid ice at −35°C into a bucket of water (1,200 g) at 45°C. Eventually, the ice all melts, and the entire system comes into thermal equilibrium. Find the final temperature of the system.
Assume a thermal equilibrium temp. T and find the heat absorbed by ice (say Q1)to raise its temp.from -35 deg. to T deg.
Similarly, find heat released by water (say Q2) when its temp. lowers from 45 deg. to T deg.
Putting Q1 = Q2 will give you T in deg. C.
Note: Do not forget to include the latent heat while computing Q1
To find the final temperature of the system after the ice has melted, we can use the principle of conservation of energy.
The formula for the conservation of energy is:
Qice + Qwater = 0
where Qice is the heat gained by the ice and Qwater is the heat lost by the water.
First, let's calculate the heat gained by the ice. We can use the equation:
Qice = mass × specific heat capacity × change in temperature
The mass of the ice is 378 g. The specific heat capacity of ice is 2.09 J/g°C. And the change in temperature is the final temperature (Tf) minus the initial temperature of the ice (Ti). As the ice is initially at -35°C, the change in temperature is Tf - (-35).
So, the heat gained by the ice is:
Qice = 378 g × 2.09 J/g°C × (Tf - (-35)).
Now, let's calculate the heat lost by the water. We can use a similar equation:
Qwater = mass × specific heat capacity × change in temperature
The mass of the water is 1200 g. The specific heat capacity of water is 4.18 J/g°C. And the change in temperature is the final temperature (Tf) minus the initial temperature of the water (Ti). As the water is initially at 45°C, the change in temperature is Tf - 45.
So, the heat lost by the water is:
Qwater = 1200 g × 4.18 J/g°C × (Tf - 45).
Since the total amount of heat gained by the ice must be equal to the total amount of heat lost by the water in order for thermal equilibrium to be reached, we can set up the equation:
Qice = -Qwater [note the negative sign indicating opposite directions of heat transfer]
378 g × 2.09 J/g°C × (Tf - (-35)) = -1200 g × 4.18 J/g°C × (Tf - 45)
Now we can solve this equation for Tf, which will give us the final temperature of the system.