Question

A thermometer reading 7degreesC is brought into a room with a constant temperature of 30 degrees C. If the thermometer reads 16degreesC after 2 ​minutes, what will it read after being in the room for 4 ​minutes? For 9 ​minutes?

Answer 1

Answer:

a) u(x) =21.47°C

b) u(x) =27.53°C

Explanation:

This requires Newton's Law of Cooling. The formula is:  

u(x) = T + (T₀ - T)×e^(kt)  

Plugging in our information:  

u(x) = 30 + (7- 30)×e^(kt)  

u(x) = 30 - 23×e^(kt)  

at temperature 16°C at time 2 min.

16 = 30 - 23×e^(2 k)  

e^(2k) = 14/23  

2k = ln(14/23)  

k = - 0.248

Temperature at t= 4 minute

u(x) = 30 - 23×e^(-0.248×4)  

u(x) =21.47°C

temperature at  t = 9 min

u(x) = 30 - 23×e^(-0.248×9)

u(x) =27.53°C