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16.07.2022 - 22:17

A portable coffee heater supplies a potential difference of 12.0 V across a Nichrome heating element with a resistance of 2.00|Omega. (a) Calculate the power consumed by the heater. (b) How many minutes would it take to heat 1.00 kg of coffee from 20.0 C

Question:

A portable coffee heater supplies a potential difference of 12.0 V across a Nichrome heating element with a resistance of 2.00 {eq}Omega {/eq}.

(a) Calculate the power consumed by the heater.

(b) How many minutes would it take to heat 1.00 kg of coffee from 20.0{eq}^{circ} {/eq}C to 50.0{eq}^{circ} {/eq}C with this heater? Coffee has a specific heat of 4 184 J/(kg {eq}^{circ} {/eq}C). Neglect any energy losses to the environment.

Answers (0)

Diana April 17, 2023 в 16:34

(a) The power consumed by the heater can be calculated using the formula: P = V^2/R where P is power, V is potential difference, and R is resistance. Substituting the given values, we get: P = (12.0 V)^2/2.00 ? P = 72.0 W Therefore, the power consumed by the heater is 72.0 W. (b) The amount of heat required to raise the temperature of 1.00 kg of coffee from 20.0°C to 50.0°C can be calculated using the formula: Q = mc?T where Q is heat, m is mass, c is specific heat, and ?T is change in temperature. Substituting the given values, we get: Q = (1.00 kg)(4184 J/(kg°C))(50.0°C - 20.0°C) Q = 1.00 ? 10^5 J The time taken to supply this amount of heat can be calculated using the formula: t = Q/P where t is time and P is power. Substituting the calculated values, we get: t = 1.00 ? 10^5 J/72.0 W t ? 1390 s Therefore, it would take \approx imately 1390 s or 23 minutes to heat 1.00 kg of coffee from 20.0°C to 50.0°C with this heater.

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