Question

use your data, the equation to the right, and the specific heat of water (4.184 j/g°c) to compute the specific heat values of each metal. use a calculator and round to the nearest hundredth place.
aluminum: c = j/g°c
copper: c = j/g°c
iron: c = j/g°c
lead: c = j/g°c
be sure to record all of these values in the data table.

Explanation:

Step1: Calculate specific heat of Aluminum

Using the formula \(c_{metal}=\frac{-c_{water}m_{water}\Delta T_{water}}{m_{metal}\Delta T_{metal}}\), substitute \(c_{water} = 4.184\space J/g^{\circ}C\), \(m_{water}=39.85\space g\), \(\Delta T_{water} = 4.7^{\circ}C\), \(m_{metal}=11.98\space g\), \(\Delta T_{metal}=- 72.9^{\circ}C\)

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Step2: Calculate specific heat of Copper

Substitute \(c_{water} = 4.184\space J/g^{\circ}C\), \(m_{water}=40.13\space g\), \(\Delta T_{water} = 1.9^{\circ}C\), \(m_{metal}=12.14\space g\), \(\Delta T_{metal}=-75.4^{\circ}C\)

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Step3: Calculate specific heat of Iron

Substitute \(c_{water} = 4.184\space J/g^{\circ}C\), \(m_{water}=40.24\space g\), \(\Delta T_{water} = 2.4^{\circ}C\), \(m_{metal}=12.31\space g\), \(\Delta T_{metal}=-75.1^{\circ}C\)

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Step4: Calculate specific heat of Lead

Substitute \(c_{water} = 4.184\space J/g^{\circ}C\), \(m_{water}=39.65\space g\), \(\Delta T_{water} = 0.7^{\circ}C\), \(m_{metal}=12.46\space g\), \(\Delta T_{metal}=-76.7^{\circ}C\)

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Answer:

Aluminum: \(c = 0.90\space J/g^{\circ}C\)
Copper: \(c = 0.35\space J/g^{\circ}C\)
Iron: \(c = 0.44\space J/g^{\circ}C\)
Lead: \(c = 0.12\space J/g^{\circ}C\)