.100 KG of an unknown metal at 94°C is placed in 100 g of water at 10°C the final temperature of the metal and water are at 70°C what is the heat capacity of the unknown metal
heat lost by mtal + heat gained by H2O = 0
[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute the numbers and solve for specific heat metal which is the only unknown in the equation.
Be careful with the units. If you use the water as 100 g I would change the metal from kg to grams.
To determine the heat capacity of the unknown metal, we can use the principle of heat transfer:
Q = mcΔT
where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, the heat transferred to the water will be equal to the heat transferred from the metal:
Qwater = Qmetal
Since we know the mass and final temperature of both the metal and water, we can calculate the heat transferred to the water:
Qwater = mwater * cwater * ΔTwater
Qwater = (100 g) * (4.18 J/g°C) * (70°C - 10°C)
Qwater = 100 g * 4.18 J/g°C * 60°C
Qwater = 25080 J
Since Qwater = Qmetal, we can also calculate the heat transferred from the metal:
Qmetal = Qwater = 25080 J
Next, we can calculate the heat capacity of the unknown metal:
Qmetal = mm * cm * ΔTmetal
Where mm is the mass of the metal and cm is the specific heat capacity of the metal.
Since we don't know the specific heat capacity of the metal, we can rearrange the equation to solve for cm:
cm = Qmetal / (mm * ΔTmetal)
cm = 25080 J / (100 kg * (70°C - 94°C))
cm = 25080 J / (100 kg * (-24°C))
cm = 25080 J / (-2400 kg°C)
cm ≈ -10.45 J/kg°C
The calculated heat capacity of the unknown metal is approximately -10.45 J/kg°C. Note that the negative sign indicates that the metal releases heat when its temperature decreases.
To determine the heat capacity of the unknown metal, we can use the equation:
Q = mcΔT
where Q is the heat transferred, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
In this case, we need to calculate the heat transferred by the unknown metal to the water. Since the final temperature of the metal and water is 70°C, the change in temperature (ΔT) for both substances is:
ΔT = final temperature - initial temperature
= 70°C - 10°C
= 60°C
The mass of the water (m1) is given as 100 g, and the specific heat capacity of water (c1) is approximately 4.18 J/g°C.
First, let's calculate the heat transferred by the water:
Q1 = m1 * c1 * ΔT
= 100 g * 4.18 J/g°C * 60°C
= 25080 J
Next, we can use the equation to determine the heat capacity of the unknown metal:
Q = mcΔT
Since the heat transferred by the metal (Q) is the same as the heat transferred to the water (Q1), we can rewrite the equation as:
Q1 = mcΔT
Rearranging the equation to solve for c:
c = Q1 / (m * ΔT)
Substituting the values:
c = 25080 J / (100 kg * 60°C)
c = 4.18 J/g°C
Therefore, the heat capacity of the unknown metal is approximately 4.18 J/g°C.