A thermometer at initial temperature is placed in a room held at constant temperature

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Ordinary differential equations · Ordinary differential equations

Computational Physics, Ch Letting the computer do the algebra

Problem

A thermometer at initial temperature

T_0 = 95.0\,\mathrm{^\circ C}

is placed in a room held at constant temperature

T_{\rm env} = 20.0\,\mathrm{^\circ C}

. Its reading obeys Newton's law of cooling,

\frac{\mathrm{d}T}{\mathrm{d}t} = -k(T-T_{\rm env}),

with cooling constant

k = 0.045\,\mathrm{s^{-1}}

and

t

measured in seconds from the moment it is placed in the room. (a) Separate the variables symbolically and integrate to obtain

T(t)

in closed form, using

T(0)=T_0

. (b) Verify your result by substituting it back into the differential equation. (c) Evaluate

T

t=30\,\mathrm{s}

, to three significant figures.

Related theory

Ordinary differential equations

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