A 2kg piece of gold metal at 90 C is placed in 5 liters (=5kg) of water at 30 C. Determine the final temperature (Tf).
To determine the final temperature (Tf) after the gold metal is placed in water, we can use the principle of heat transfer, specifically the law of conservation of energy.
The law of conservation of energy states that the total amount of energy in a closed system remains constant. In this case, when the gold metal is placed in water, energy will flow from the hotter object (the gold) to the colder object (the water) until both objects reach the same final temperature.
To calculate the final temperature, we can use the concept of heat transfer equation:
Q1 = Q2
Where:
Q1 = Heat gained by the gold
Q2 = Heat lost by the water
The heat gained by the gold can be calculated using the specific heat capacity formula:
Q1 = mcΔT1
Where:
m = mass of the gold (2kg)
c = specific heat of gold
ΔT1 = change in temperature for the gold (Tf - 90)
The heat lost by the water can be calculated using the specific heat capacity formula:
Q2 = mcΔT2
Where:
m = mass of the water (5kg)
c = specific heat of water
ΔT2 = change in temperature for the water (Tf - 30)
Since the final temperature (Tf) is the same for both gold and water, we can set up an equation and solve for Tf:
mcΔT1 = mcΔT2
For the purposes of this calculation, we assume that the specific heat capacities of the gold and water remain constant over the given temperature range.
Now, we can substitute the known values into the equation:
2c(Tf - 90) = 5c(Tf - 30)
Simplifying this equation:
2Tf - 180 = 5Tf - 150
3Tf = 30
Tf = 10°C
Therefore, the final temperature (Tf) when the gold metal is placed in water is 10°C.