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tonny07

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A copper plate is heated to a temperature of 100 degree C. At time t = 0 , it is immersed in water that is maintained at a temperature of 30 degree C. After 3 minutes the temperature of the plate is reduced to 70 degree C. Suppose that this problem is governed by Newton’s Law equation
dT = k (T 30)
dt

where T is the temperature and k is the unknown constant. Find the time at which the temperature of the plate is reduced to 31 degree C.
 
tonny07 said:
A copper plate is heated to a temperature of 100 degree C. At time t = 0 , it is immersed in water that is maintained at a temperature of 30 degree C. After 3 minutes the temperature of the plate is reduced to 70 degree C. Suppose that this problem is governed by Newton’s Law equation
dT/dt = k (T - 30)

where T is the temperature and k is the unknown constant. Find the time at which the temperature of the plate is reduced to 31 degree C.
Click to expand...

The solution to the ODE should be

T = 30 + C* e[sup:11u8ywm5]kt[/sup:11u8ywm5]

Solve for C and k - from the given condition at t=0 and t=3

Then solve for 't' when T = 31
 
tonny07 said:
t = 22 minute 48 seconds.

it's the correct answer?
Click to expand...

I get

t = 22 minute 46.52531979 seconds.

If you are keeping time in minutes only - then you could call that 23 minutes.
 
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