A copper rod that has a mass of 200.0 g has an initial temperature of [tex]$20.0^{\circ} C$[/tex] and is heated to [tex]$40.0^{\circ} C$[/tex]. If [tex]$1,540 J$[/tex] of heat are needed to heat the rod, what is the specific heat of copper?
Use [tex]$q=m C_p \Delta T$[/tex].
A. [tex]$0.0130 J /( g { }^{\circ} C )$[/tex]
B. [tex]$0.0649 J /( g { }^{\circ} C )$[/tex]
C. [tex]$0.193 J /( g { }^{\circ} C )$[/tex]
D. [tex]$0.385 J /( g { }^{\circ} C )$[/tex]
Answer (1)
Calculate the change in temperature: Δ T = 40. 0 ∘ C − 20. 0 ∘ C = 20. 0 ∘ C .
Rearrange the formula to solve for specific heat: C p = m Δ T q .
Substitute the given values: C p = ( 200.0 g ) ( 20. 0 ∘ C ) 1540 J .
Calculate the specific heat of copper: 0.385 J / ( g ∘ C ) .
Explanation
Understanding the Problem We are given the mass of a copper rod, its initial and final temperatures, and the amount of heat required to raise its temperature. We are asked to find the specific heat of copper. We will use the formula q = m C p Δ T , where q is the heat added, m is the mass, C p is the specific heat, and Δ T is the change in temperature.
Calculating the Change in Temperature First, we need to calculate the change in temperature, Δ T . This is given by the final temperature minus the initial temperature: Δ T = T f − T i = 40. 0 ∘ C − 20. 0 ∘ C = 20. 0 ∘ C
Rearranging the Formula Next, we rearrange the formula q = m C p Δ T to solve for the specific heat, C p : C p = m Δ T q
Substituting the Values Now, we substitute the given values into the equation: C p = ( 200.0 g ) ( 20. 0 ∘ C ) 1540 J = 4000 1540 J / ( g ⋅ ∘ C ) = 0.385 J / ( g ⋅ ∘ C )
Final Answer Therefore, the specific heat of copper is 0.385 J / ( g ⋅ ∘ C ) .
Examples
Specific heat capacity is a fundamental concept in thermodynamics, crucial for understanding how different materials respond to heating. For instance, when designing cookware, engineers consider the specific heat capacity of the materials to ensure even heat distribution and prevent burning. Copper, with its relatively high specific heat, is often used in cookware bases to efficiently transfer heat from the stove to the food, ensuring consistent cooking temperatures.
