The value of D and a in T(t)=T(0)+Dat.
To estimate the temperature of
EunoR
Answered question
2021-09-25
The value of D and a in .
To estimate the temperature of pan after 10 minutes.
The time taken by pan to reach 400 F.
Answer & Explanation
SoosteethicU
Skilled2021-09-26Added 102 answers
Given:
and T0 is 320 F. Boiling water with a temperature of 2120 and it cools to 700 in 30 minutes. Here D is the difference between room temperature and water temperature.
Calculation:
a) To determine the value of D and a:
We have ----(1).
Here ----(2)
Water temperature is 2120F
Hence ,
Next, and minutes and hour.
Substitute the above values in the equation (1),
Here . On substituting the value of T(12) in the above we get,
.
Hence the values of D, T0 and a are 180, 32 and 0.044 respectively.
b) To estimate the temperature of pan after 10 minutes.
Here 10 minutes hour. So, .
Substitute the value of t, a, D and t0 in the equation (1) we get,
Hence the value of T(t) after 10 minutes is 1390F.
c) The time taken by pan to reach 400 F.
Given: and .
Substitute the above values in equation (1) we get,
Applying log on both sides,
Hence the time taken by pan to reach 400 F is 1 hour.
Conclusion:
The value of D is 180, a is 0.044 and T0 is 320 F. The temperature of the pan after 10 minutes is 1390 F. The time taken by pan to reach 400 F is 1 hour.