Three metals, iron, copper, and gold, have heat capacities of 0.450 J/goC, 0.385 J/goC and 0.129 J/goC, respectively. A 10g sample of each metal was heated in a water bath at 100oC. One of these metals will be placed in a Styrofoam cup containing 50.0 mL of water at 25oC. Which metal should be placed in the cup if we want to observe the lowest temperature change in the water?
The water will be heated by each metal. How much.
q = mass H2O x specific heat H2O x delta T.
Therefore for dT to be the smallest, you want q to be the smallest
How much will the metal change?
q = mass metal x specific heat metal x (Tfinal-Tinitial)
q = 10g x specific heat metal x (Tfinal - 100). If you want q to be the smallest, what does that say about specific heat, all other things being constant?
To determine which metal should be placed in the cup to observe the lowest temperature change in the water, we need to compare the heat capacities of the metals.
The formula for calculating the heat transferred (Q) is:
Q = m * c * ΔT
Where:
Q = heat transferred
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
In this case, we have a 10g sample of each metal heated in a water bath at 100oC. Since we want to observe the lowest temperature change in the water, we need to find the metal with the lowest value of Q.
For each metal, we can calculate the heat transferred by using the formula above. Since the initial temperature of the water is 25oC, and the final temperature will be some value below 100oC, we can set the value of ΔT as 100oC in the calculations.
Let's calculate the heat transferred for each metal:
For iron:
Q(iron) = m * c(iron) * ΔT
= 10g * 0.450 J/goC * 100oC
= 450 J
For copper:
Q(copper) = m * c(copper) * ΔT
= 10g * 0.385 J/goC * 100oC
= 385 J
For gold:
Q(gold) = m * c(gold) * ΔT
= 10g * 0.129 J/goC * 100oC
= 129 J
From the calculations, we can see that the heat transferred for iron is the highest (450 J), followed by copper (385 J), and gold (129 J). Therefore, the metal that should be placed in the cup to observe the lowest temperature change in the water is gold.