The lowest temperature ever recorded in Alaska is-6 C. The highest temperature ever recorded in Alaska is 38°C. Suppose a piece of metal with a mass of 180 g and a temperature of -62.0°C is placed in a calorimeter containing 0.500 kg of water with a temperature of 38.0°C. If the final equilibrium temperature of the metal and water is 36.9°C, what is the specific heat capacity of the metal? Use the calculated value of the specific heat capacity to identify the metal.
The answer is 130 but I don't get how you solve the problem.
https://www.jiskha.com/questions/1815862/the-lowest-temperature-ever-recorded-in-alaska-is-6-c-the-highest-temperature-ever
by the way the lowest temp recorded in Alaska is below the lowest in Boston, not -6C
To solve this problem, we can make use of the principle of heat transfer and the equation for heat transfer:
Q = mcΔT
where Q is the heat transfer, m is the mass of the substance, c is the specific heat capacity, and ΔT is the change in temperature.
In this case, the heat gained by the water will be equal to the heat lost by the metal (since they reach thermal equilibrium):
Qwater = Qmetal
The heat gained by the water can be calculated using the equation:
Qwater = mwater * cwater * ΔTwater
Similarly, the heat lost by the metal can be calculated using the equation:
Qmetal = mmetal * cmetal * ΔTmetal
Given that the final equilibrium temperature is 36.9°C, we can calculate the changes in temperature for both the water and metal:
ΔTwater = 36.9°C - 38.0°C = -1.1°C
ΔTmetal = 36.9°C - (-62.0°C) = 98.9°C
Plugging in the known values, we have:
mwater * cwater * ΔTwater = mmetal * cmetal * ΔTmetal
Substituting the given values:
(0.500 kg) * (cwater) * (-1.1°C) = (0.180 kg) * (cmetal) * (98.9°C)
Simplifying and solving for cmetal:
0.55 * cwater = 17.802 * cmetal
cmetal / cwater = 0.55 / 17.802
cmetal = (0.55 / 17.802) * cwater
Now, to find the specific heat capacity of the metal, we need to know the specific heat capacity of water. The specific heat capacity of water is approximately 4.18 J/g°C.
Substituting this value:
cmetal = (0.55 / 17.802) * 4.18 J/g°C
cmetal ≈ 0.130 J/g°C
Therefore, the specific heat capacity of the metal is approximately 0.130 J/g°C.
To identify the metal, we can compare the calculated specific heat capacity to known values. This requires referencing a table of specific heat capacities for different metals and finding the closest match to 0.130 J/g°C.