120 grams of an unknown metal at a temperature of 95 degrees celcuius is poured into 140 grams of aluminum calorimeter containing 220 grams of water. If the inital temperature of the water and calorimeter was 15 degree celcuius and the final temperature was 18 celcius, find the specfic heat of metal. the specfic heat of aluminum is .22 calories/gams Celcius. The specfic heat of water is 1.00 calorie /gram Celcius
To find the specific heat of the unknown metal, follow this step-by-step calculation:
Step 1: Calculate the heat gained by the water and calorimeter:
Qwater = mwater * cwater * ΔTwater
where:
- mwater is the mass of water (220 grams)
- cwater is the specific heat of water (1.00 calorie/gram Celsius)
- ΔTwater is the change in temperature of the water (final temperature - initial temperature)
= 18 Celsius - 15 Celsius = 3 Celsius
Qwater = 220 * 1.00 * 3 = 660 calories
Qcalorimeter = mcalorimeter * cAluminum * ΔTcalorimeter
where:
- mcalorimeter is the mass of the calorimeter (140 grams)
- cAluminum is the specific heat of aluminum (0.22 calorie/gram Celsius)
- ΔTcalorimeter is the change in temperature of the calorimeter (final temperature - initial temperature) = 18 Celsius - 15 Celsius = 3 Celsius
Qcalorimeter = 140 * 0.22 * 3 = 92.4 calories
Step 2: Calculate the heat lost by the unknown metal:
Qmetal = mm etal * cmetal * ΔTmetal
where:
- mmetal is the mass of the unknown metal (120 grams)
- cmetal is the specific heat of the unknown metal (to be determined)
- ΔTmetal is the change in temperature of the unknown metal (final temperature - initial temperature) = 18 Celsius - 95 Celsius = -77 Celsius
Qmetal = 120 * cmetal * (-77)
Step 3: The total heat gained by the water, calorimeter, and the heat lost by the metal should be equal since the system is isolated. Therefore:
Qwater + Qcalorimeter = Qmetal
Substituting the calculated values:
660 + 92.4 = 120 * cmetal * (-77)
Step 4: Solve for the specific heat of the unknown metal (cmetal):
(660 + 92.4) / (-92.4) = cmetal
cmetal ≈ -7.474
Note: The negative sign arises because the metal loses heat (negative value) while the water and calorimeter gain heat (positive value). However, specific heat is generally reported as a positive value, so we neglect the negative sign.
Therefore, the specific heat of the unknown metal is approximately 7.474 calorie/gram Celsius.