Use your data, the equation to the right, and the specific heat of water ([tex]$4.184 J / g ^{\circ} C$[/tex]) to compute the specific heat values of each metal. Use a calculator and round to the nearest hundredth place.

Aluminum: [tex]$c=$[/tex] $\square$ [tex]$J / g ^{\circ} C$[/tex]

Copper: [tex]$c=$[/tex] $\square$ [tex]$3 / g ^{\circ} C$[/tex]

Iron: [tex]$c=$[/tex] $\square$ [tex]$J / g ^{\circ} C$[/tex]

Lead: [tex]$c=$[/tex] $\square$ [tex]$30^{\circ} C$[/tex]

Be sure to record all of these values in the data table.

[tex]$c_{\text {metal }}=\frac{-c_{\text {water }} m_{\text {water }} \Delta T_{\text {water }}}{m_{\text {metal }} \Delta T_{\text {metal }}}$[/tex]

To calculate the specific heat of metals, use the formula c m e t a l ​ = m m e t a l ​ ⋅ Δ T m e t a l ​ − c w a t er ​ ⋅ m w a t er ​ ⋅ Δ T w a t er ​ ​ . The expected specific heat values after calculations are Aluminum: 0.22, Copper: 0.39, Iron: 0.45 and Lead: 0.13 J/g°C, depending on accurate measurements of mass and temperature changes.
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Answered by Anonymous | 2025-07-07

Calculate the specific heat for Aluminum: c A l ​ ≈ 0.22 J / g ∘ C .
Calculate the specific heat for Copper: c C u ​ ≈ 0.35 J / g ∘ C .
Calculate the specific heat for Iron: c F e ​ ≈ 0.44 J / g ∘ C .
Calculate the specific heat for Lead: c P b ​ ≈ 0.12 J / g ∘ C .
The specific heat values for each metal are: Aluminum: 0.22 ​ J / g ∘ C , Copper: 0.35 ​ J / g ∘ C , Iron: 0.44 ​ J / g ∘ C , Lead: 0.12 ​ J / g ∘ C .

Explanation

Problem Analysis We are given the specific heat of water ( c w a t er ​ = 4.184 J / g ∘ C ) and the formula to calculate the specific heat of a metal: c m e t a l ​ = m m e t a l ​ Δ T m e t a l ​ − c w a t er ​ m w a t er ​ Δ T w a t er ​ ​ . We also have a table with the mass of water ( m w a t er ​ ), mass of metal ( m m e t a l ​ ), change in temperature of water ( Δ T w a t er ​ ), and change in temperature of the metal ( Δ T m e t a l ​ ) for Aluminum, Copper, Iron, and Lead. Our goal is to calculate the specific heat ( c ) for each metal using the provided formula and data, rounding each result to the nearest hundredth.

Calculating Specific Heat of Aluminum First, let's calculate the specific heat for Aluminum ( c A l ​ ). We substitute the given values into the formula: c A l ​ = ( 11.98 g ) ( − 72. 9 ∘ C ) − ( 4.184 J / g ∘ C ) ( 9.85 g ) ( 4. 7 ∘ C ) ​ After performing the calculation, we find that c A l ​ ≈ 0.22 J / g ∘ C .

Calculating Specific Heat of Copper Next, we calculate the specific heat for Copper ( c C u ​ ). We substitute the given values into the formula: c C u ​ = ( 12.14 g ) ( − 75. 4 ∘ C ) − ( 4.184 J / g ∘ C ) ( 40.13 g ) ( 1. 9 ∘ C ) ​ After performing the calculation, we find that c C u ​ ≈ 0.35 J / g ∘ C .

Calculating Specific Heat of Iron Now, we calculate the specific heat for Iron ( c F e ​ ). We substitute the given values into the formula: c F e ​ = ( 12.31 g ) ( − 75. 1 ∘ C ) − ( 4.184 J / g ∘ C ) ( 40.24 g ) ( 2. 4 ∘ C ) ​ After performing the calculation, we find that c F e ​ ≈ 0.44 J / g ∘ C .

Calculating Specific Heat of Lead Finally, we calculate the specific heat for Lead ( c P b ​ ). We substitute the given values into the formula: c P b ​ = ( 12.46 g ) ( − 76. 7 ∘ C ) − ( 4.184 J / g ∘ C ) ( 39.65 g ) ( 0. 7 ∘ C ) ​ After performing the calculation, we find that c P b ​ ≈ 0.12 J / g ∘ C .

Final Answer Therefore, the specific heat values for each metal, rounded to the nearest hundredth, are: Aluminum: 0.22 J / g ∘ C Copper: 0.35 J / g ∘ C Iron: 0.44 J / g ∘ C Lead: 0.12 J / g ∘ C


Examples
Understanding specific heat is crucial in many real-world applications. For example, when designing engines, engineers need to know the specific heat of the metals they use to predict how the engine components will heat up and cool down. This knowledge helps them choose the right materials and design efficient cooling systems. Similarly, in cooking, different pots and pans made of different materials heat up at different rates due to their specific heats, affecting how quickly and evenly food cooks. By understanding specific heat, we can make informed decisions in various fields, from engineering to everyday cooking.

Answered by GinnyAnswer | 2025-07-07