Newton's law of cooling states that the rate at which a body cools is proportional to the difference in temperature between the body (8) and its surrounding environment (T). A body is exposed to a constant surrounding temperature of (280 + Q/5) Kelvin (K). (a) Formulate the differential equation governing this system, then solve for body temperature O using two different methods. (b) After 1 minute the temperature of the body is 315 K and after 5 minutes it is 310 K. Determine the particular solution of 0. (c) Sketch the graph of 0 against t from 0 to 10 minutes. Comment upon your graph.

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Newton's law of cooling states that the rate at which a body cools is proportional to the difference
in temperature between the body (8) and its surrounding environment (T). A body is exposed to a
constant surrounding temperature of (280 + Q/5) Kelvin (K).
(a) Formulate the differential equation governing this system, then solve for body temperature
O using two different methods.
(b) After 1 minute the temperature of the body is 315 K and after 5 minutes it is 310 K.
Determine the particular solution of 0.
(c) Sketch the graph of 0 against t from 0 to 10 minutes. Comment upon your graph.
Transcribed Image Text:Newton's law of cooling states that the rate at which a body cools is proportional to the difference in temperature between the body (8) and its surrounding environment (T). A body is exposed to a constant surrounding temperature of (280 + Q/5) Kelvin (K). (a) Formulate the differential equation governing this system, then solve for body temperature O using two different methods. (b) After 1 minute the temperature of the body is 315 K and after 5 minutes it is 310 K. Determine the particular solution of 0. (c) Sketch the graph of 0 against t from 0 to 10 minutes. Comment upon your graph.
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