A small toaster that operates at 120 V has a heating element made from a 4.4-m-long, 0.70-mm-diameter nichrome wire. The resistivity, density, and specific heat of nichrome are, respectively, 1.5 x 10⁻⁶ Ωm, 8400 kg/m³, and 450 J/kg K. If half the heat energy is lost to the air, how long does it take the heating element to warm from 20℃ to 450℃, about the temperature at which it first begins to glow red?

검증된 단계별 안내

Determine the resistance of the nichrome wire using the formula for resistance:

R = \frac{ρ}{L} .

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

13m

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Ohm's Law

Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. This relationship is expressed as V = IR, where V is voltage, I is current, and R is resistance. Understanding this law is crucial for analyzing electrical circuits, such as the toaster's heating element, to determine how much current flows at a given voltage.

Heat Transfer and Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. In this context, it helps determine how much energy is needed to heat the nichrome wire from 20℃ to 450℃. Additionally, understanding heat transfer mechanisms, including conduction, convection, and radiation, is essential for calculating energy losses to the surrounding air, which affects the heating time.

Resistivity and Resistance

Resistivity is a material property that quantifies how strongly a given material opposes the flow of electric current, expressed in ohm-meters (Ωm). The resistance of a wire can be calculated using the formula R = ρ(L/A), where ρ is resistivity, L is the length of the wire, and A is its cross-sectional area. This concept is vital for determining how much electrical energy is converted into heat in the toaster's heating element, influencing its performance and efficiency.