a sheet of gold weighing 10.0g and at a temperature of 18.0 degrees c is placed flat on a sheet of iron weighing 20.0g and a tenp. of 55.6 degrees c. what is the final temp. of the combined metals? assume that no heat is lost to the surroundings.
To find the final temperature of the combined metals, we can use the principle of heat transfer known as calorimetry. The formula for calorimetry is:
m1c1(T1 - Tf) = m2c2(Tf - T2)
Where:
m1 = mass of gold (10.0g)
c1 = specific heat capacity of gold (0.13 J/g°C)
T1 = initial temperature of gold (18.0°C)
Tf = final temperature of the combined metals (unknown)
m2 = mass of iron (20.0g)
c2 = specific heat capacity of iron (0.45 J/g°C)
T2 = initial temperature of iron (55.6°C)
Let's plug in the values and solve for Tf:
10.0g * 0.13 J/g°C * (18.0°C - Tf) = 20.0g * 0.45 J/g°C * (Tf - 55.6°C)
Simplifying the equation:
1.3 J/°C * (18.0°C - Tf) = 9 J/°C * (Tf - 55.6°C)
19.4 J - 1.3 J * Tf = 9J * Tf - 501.6 J
10.3 J * Tf = 481.4 J
Tf = 46.8°C
Therefore, the final temperature of the combined metals is 46.8°C.
To find the final temperature of the combined metals, we can use the principle of heat transfer, specifically the equation for heat transfer known as the calorimetry equation:
Q = mcΔT
Where:
Q: Heat transfer (in joules or calories)
m: Mass of the substance (in grams)
c: Specific heat capacity of the substance (in J/g°C or cal/g°C)
ΔT: Change in temperature (in °C)
In this case, we have two metals, gold and iron, and we are assuming no heat loss to the surroundings. Therefore, the heat gained by the gold must equal the heat lost by the iron.
First, let's calculate the heat absorbed by the gold and the heat lost by the iron:
Heat gained by gold = Heat lost by iron
m_gold * c_gold * ΔT_gold = m_iron * c_iron * ΔT_iron
Where:
m_gold = Mass of gold (10.0g)
m_iron = Mass of iron (20.0g)
c_gold = Specific heat capacity of gold (0.13 J/g°C)
c_iron = Specific heat capacity of iron (0.45 J/g°C)
ΔT_gold = Final temperature - Initial temperature of gold (Unknown)
ΔT_iron = Initial temperature of iron - Final temperature (Unknown)
Next, we substitute the given values and the unknown variables back into the equation:
10.0g * 0.13 J/g°C * (ΔT_gold) = 20.0g * 0.45 J/g°C * (55.6 - ΔT_gold)
Simplifying the equation:
1.3 J/°C * ΔT_gold = 9 J/°C * (55.6 - ΔT_gold)
1.3 ΔT_gold = 9 * 55.6 - 9 ΔT_gold
1.3 ΔT_gold + 9 ΔT_gold = 9 * 55.6
10.3 ΔT_gold = 500.4
ΔT_gold = 500.4 / 10.3
ΔT_gold ≈ 48.54°C
Now, to find the final temperature of the combined metals, we need to subtract ΔT_gold from the initial temperature of the gold:
Final temperature = Initial temperature of gold - ΔT_gold
Final temperature = 18.0°C - 48.54°C
Final temperature ≈ -30.54°C
Therefore, the final temperature of the combined metals is approximately -30.54°C.
heat absorbed by gold + heat lost b Fe = 0
[mass Au x specific heat Au x (Tfinal-Tintial)] + [mass Fe x specific heat Fe x (Tfinal-Tintial)] = 0
Tfinal is the only unknown.