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Chapter 19: Problem 1

Estimate the energy required to raise the temperature of \(2 \mathrm{~kg}\left(4.42 \mathrm{lb}_{\mathrm{m}}\right)\) of the following materials from 20 to \(100^{\circ} \mathrm{C}\) (68 to,

Short Answer

Expert verified
Answer: To raise the temperature of 2 kg of iron and water to 100°C from 20°C, 72,000 J of energy is required for iron and 672,000 J for water.

Step by step solution

01

Calculate change in temperature for each material

ΔT = Final temperature - Initial temperature ΔT = 100°C - 20°C = 80°C
02

Calculate the energy required for iron

We are given the specific heat capacity of iron as \(c_{iron} = 450 \mathrm{~J/kg·°C}\). Using the energy formula: Q_iron = m × c_{iron} × ΔT Q_iron = 2 kg × 450 J/kg·°C × 80°C Q_iron = 72000 J The energy required to raise the temperature of 2 kg of iron from 20°C to 100°C is 72,000 J.
03

Calculate the energy required for water

We are given the specific heat capacity of water as \(c_{water} = 4200 \mathrm{~J/kg·°C}\). Using the energy formula: Q_water = m × c_{water} × ΔT Q_water = 2 kg × 4200 J/kg·°C × 80°C Q_water = 672000 J The energy required to raise the temperature of 2 kg of water from 20°C to 100°C is 672,000 J. The energy required to heat iron from 20°C to 100°C is 72,000 J, and for water, it is 672,000 J.

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Most popular questions from this chapter

For some ceramic materials, why does the thermal conductivity first decrease and then increase with rising temperature?

The constant \(A\) in Equation \(19.2\) is \(12 \pi^{4} R / 5 \theta_{\mathrm{D}}^{3}\), where \(R\) is the gas constant and \(\theta_{\mathrm{D}}\) is the Debye temperature \((\mathrm{K})\). Estimate \(\theta_{\mathrm{D}}\) for copper, given that the specific heat is \(0.78 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) at \(10 \mathrm{~K}\).

(a) Briefly explain why \(C_{v}\) rises with increasing temperature at temperatures near \(0 \mathrm{~K}\). (b) Briefly explain why \(C_{v}\) becomes virtually independent of temperature at temperatures far removed from \(0 \mathrm{~K}\).

Briefly explain thermal expansion using the potential-energy-versus- interatomic-spacing curve.

For each of the following pairs of materials, decide which has the larger thermal conductivity. Justify your choices. (a) Pure copper; aluminum bronze (95 wt \% Cu-5 wt \(\% \mathrm{Al})\) (b) Fused silica; quartz (c) Linear polyethylene; branched polyethylene (d) Random poly(styrene-butadiene) copolymer; alternating poly(styrene- butadiene) copolymer
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