Final answer:
The final temperature of the coffee after the ice melts is 95°C.
Step-by-step explanation:
To find the final temperature of the coffee after the ice melts, we need to calculate the amount of heat gained by the ice cube and the amount of heat lost by the coffee. The heat gained by the ice is equal to the heat lost by the coffee. The formula for heat transfer is:
q = m·c·ΔT
Where q is the amount of heat transferred, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
First, let's find the heat gained by the ice:
qice = mice·cice·ΔTice
Given that the mass of the ice is 9.5 g, the specific heat capacity of ice is 2.062 J/(g·°C), and the change in temperature of the ice is the melting point of ice (0°C), we can calculate:
qice = (9.5 g)·(2.062 J/(g·°C))·(0°C - 0°C) = 0 J
The heat gained by the ice cube is 0 J, meaning no heat is transferred to or from the ice during its melting process.
Next, let's find the heat lost by the coffee:
qcoffee = mcoffee·ccoffee·ΔTcoffee
Given that the mass of the coffee is 130 g, the specific heat capacity of water/coffee is 4.184 J/(g·°C), and the change in temperature of the coffee is the initial temperature of the coffee (95°C) minus the final temperature of the coffee, we can calculate:
qcoffee = (130 g)·(4.184 J/(g·°C))·(95°C - Tfinal)
Since the heat gained by the ice is equal to the heat lost by the coffee:
qice = qcoffee
we can substitute the values and solve for the final temperature of the coffee:
0 J = (130 g)·(4.184 J/(g·°C))·(95°C - Tfinal)
Simplifying the equation:
(130 g)·(4.184 J/(g·°C))·(95°C - Tfinal) = 0 J
Dividing both sides of the equation by (130 g)·(4.184 J/(g·°C)):
95°C - Tfinal = 0
Subtracting 95°C from both sides:
-Tfinal = -95°C
Multiplying both sides by -1:
Tfinal = 95°C
The final temperature of the coffee after the ice melts is 95°C.