The temperature (in degrees Celsius) of a small object cooling in a room of constant…
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
The temperature T (in degrees Celsius) of a small object cooling in a room of constant temperature 25∘C satisfies a differential equation whose slope field is shown. Several slope segments on the T-axis (x denotes time in minutes) are measured and recorded:
T=10: slope 0.75T=20: slope 0.25T=25: slope 0
A solution curve representing the object’s temperature passes through the point (0,20).
(a) Use the slope at T=20 to estimate dtdT at time t=0.
(b) Assuming the slope remains approximately constant over the next minute, use your estimate from part (a) to approximate the object’s temperature at t=1 minute.
(c) Using only the slope values provided, explain why the temperature approaches 25∘C as t becomes large.