Assignment 4: Problem 6

Question

When a hot object is placed in a water bath whose temperature is , it cools from  to  in . In another bath, the same cooling occurs in . Find the temperature of the second bath.

The temperature of the second bath = _____________ 

Answer 1

The Newton temperature equation is:

T(t) = T_s + (T₀ - T_s ) e^(-kt)

T_s = the starting temperature

T₀ = the bath temperature (ambient temperature)

T(t) = the temperature as a function of time

For the first bath

50 = 100+(25-100)e^-150k

Solving for k:

-50=(-75)e^-150k

k = -ln(50/75)/150 = ln(3)/150 ≈ 0.0073

For the second bath

50 = 100+(T₀-100)e^-0.0073(130) e^-0.0073(130)≈0.386

-50 = 0.386T₀ - 38.6

T₀ ≈ -29.5