A thermometer reading 7 degree C is brought into a room with

A thermometer reading 7 degree C is brought into a room with a constant temperature of 29 degree C. If the theorems reads 15 degree C after 4 minutes, what will read after being in the room for 6 minutes? For 11 minutes? After 6 minutes, the thermometer will read degree C. After 11 minutes, the thermometer will read degree C

Solution

Using newton\'s law of cooling

U = T + (U0 - T)*e^(kt)

After t = 4 min

U0 = 7

T = 29

U = 15

Using these values

15 = 29 + (7 - 29)*e^(4*k)

-14 = -22*e^(4*k)

e^4k = 7/11

k = (1/4)*ln (7/11) = -0.1129

A.

Now when t = 6 min

U = 29 + (7 - 29)*e^(-0.1129*6) = 17.825 C

when t = 11 min

U = 29 + (7 - 29)*e^(-0.1129*11) = 22.645 C