50.0 G SILVER SPOON AT 20.0 C PLACED IN A CUP OF COFFEE AT 90.0C
To calculate the final temperature, we can use the principle of conservation of energy.
The equation we will use is:
mcΔT = mLΔT
Where:
m is the mass of the silver spoon (50.0 g)
c is the specific heat capacity of silver (0.235 J/g°C)
ΔT is the change in temperature
L is the latent heat of fusion for silver (79.8 J/g)
First, let's determine the amount of heat gained or lost by the silver spoon:
mcΔT = mLΔT
(50.0 g)(0.235 J/g°C)(Tf - 20.0°C) = (50.0 g)(79.8 J/g)(90.0°C - Tf)
Simplifying the equation:
11.75(Tf - 20) = 3990(90 - Tf)
11.75Tf - 235 + 3990Tf - 359100 = 0
401.75Tf = 359335
Tf = 895.71°C
Therefore, the final temperature of the silver spoon in the cup of coffee is approximately 895.71°C.
To determine the final temperature of the spoon when placed in the cup of coffee, we can use the principle of heat transfer. The heat gained by the spoon will be equal to the heat lost by the coffee. We can use the equation:
Q1 = Q2
Where:
Q1 is the heat gained by the spoon
Q2 is the heat lost by the coffee
The formula for heat transfer is:
Q = m * c * ΔT
Where:
Q is the heat transferred
m is the mass
c is the specific heat capacity
ΔT is the change in temperature
First, let's calculate the heat gained by the spoon:
Q1 = m1 * c1 * ΔT1
The mass of the spoon (m1) is given as 50.0 g, and the specific heat capacity of silver (c1) is approximately 0.235 J/g°C. The change in temperature (ΔT1) is the final temperature minus the initial temperature:
ΔT1 = Tfinal - Tinitial = 90.0°C - 20.0°C = 70.0°C
Substituting the values:
Q1 = 50.0 g * 0.235 J/g°C * 70.0°C
Let's calculate Q1:
Q1 = 820.5 J
Now, let's calculate the heat lost by the coffee:
Q2 = m2 * c2 * ΔT2
The mass of the coffee (m2) is not given, so we need this information to proceed. Once we have the mass of the coffee, we need to know the specific heat capacity of the coffee (c2). Assuming the coffee has a similar specific heat capacity to water (4.18 J/g°C), we can use this value. The change in temperature (ΔT2) is the same as before, 70.0°C.
Given the mass of the coffee, we can calculate Q2:
Q2 = m2 * 4.18 J/g°C * 70.0°C
Now, if you provide the mass of the coffee, I can help you calculate the value of Q2 and find the final temperature of the spoon.