Body cooling from 70°C to 50°C in 6 minutes using Newton's law of cooling

[dan4loriel]

Homework Statement

please i need help as have been trying to solve this question: A body cools from 70°C to 50°C in 6mins when the temp of the surrounding is 30°C. what wil be the tempt of the body after another 12mins if the cooling obeys Newtons law of cooling


equation:
dq/dt = -k(θ-θs)

where m- mass of the body
c-specific heat capacity of the body
θ-temp of the body
θs-temp of the surrounding or room

The Attempt at a Solution

i tried sovling it as follows:

dq=mc(70-50)

=20mc

dq/dt= 20mc/6= -k(70-50) =-20k

dq=mc(50-θs)
dq-dt=mc(50-θs)/12=-k

got lost from here please help!

 

[sweet springs]

Hi. by relation q=cθ the equation is

dθ/dt = -k/c (θ-θs) solving it
θ　= (θ0-θs) e^-k/c t + θs
where θ0 is initial temperature of the body.

regards.

 

[dan4loriel]

thanks for the help

 

[dan4loriel]

hey,

wouldnt mind if you help me in solving them as regards to the equation given

 

[berkeman]

Homework Statement

please i need help as have been trying to solve this question: A body cools from 70°C to 50°C in 6mins when the temp of the surrounding is 30°C. what wil be the tempt of the body after another 12mins if the cooling obeys Newtons law of cooling


equation:
dq/dt = -k(θ-θs)

where m- mass of the body
c-specific heat capacity of the body
θ-temp of the body
θs-temp of the surrounding or room

The Attempt at a Solution

i tried sovling it as follows:

dq=mc(70-50)

=20mc

dq/dt= 20mc/6= -k(70-50) =-20k

dq=mc(50-θs)
dq-dt=mc(50-θs)/12=-k

got lost from here please help!

hey,

wouldnt mind if you help me in solving them as regards to the equation given

We don't solve your homework problems for you here at the PF. We can give hints, like the one you got above. Now it is your turn to do wht work in solving the problem.

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