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Ch 19: Work, Heat, and the First Law of Thermodynamics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 19, Problema 13

How much heat energy must be added to a 6.0-cm-diameter copper sphere to raise its temperature from −50°C to 150°C?

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Determine the formula for heat energy required to raise the temperature of an object: Q = mcΔT, where Q is the heat energy, m is the mass of the object, c is the specific heat capacity of the material, and ΔT is the change in temperature.
Calculate the volume of the copper sphere using the formula for the volume of a sphere: V = 43πr3, where r is the radius of the sphere. The radius is half the diameter, so r = 6.02 = 3.0 cm.
Find the mass of the copper sphere using the formula m = ρV, where ρ is the density of copper (approximately 8.96 g/cm³). Substitute the volume calculated in the previous step.
Determine the temperature change ΔT = Tfinal - Tinitial. Here, Tfinal = 150°C and Tinitial = -50°C, so ΔT = 150 - (-50).
Substitute the values for mass, specific heat capacity of copper (approximately 0.385 J/g°C), and temperature change into the heat energy formula Q = mcΔT to calculate the total heat energy required.

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Specific Heat Capacity

Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. For copper, this value is approximately 0.385 J/g°C. Understanding this concept is crucial for calculating the heat energy needed to change the temperature of the copper sphere.
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Specific Heat & Temperature Changes

Heat Energy Calculation

The heat energy (Q) required to change the temperature of an object can be calculated using the formula Q = mcΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. This formula allows us to quantify the energy needed based on the material's properties and the desired temperature change.
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Mass of the Sphere

To apply the heat energy calculation, we need to determine the mass of the copper sphere. The mass can be calculated using the formula m = ρV, where ρ is the density of copper (approximately 8.96 g/cm³) and V is the volume of the sphere. The volume of a sphere is given by V = (4/3)πr³, where r is the radius. This step is essential for finding the total heat energy required.
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