sid_galt
Oct30-05, 11:56 PM
I want to determine the temperature of a body in space exposed to the Sun as it varies with time.
I tried this.
Let A be the area exposed to the Sun and 2A the total area of the body. Let 1380 W/m2 be the power of the sunlight falling on the body. Let \sigma be the boltzmann constant, \epsilon the emissivity of the body and T the temperature at a a particular instant of time, m the mass of the body and C the specific heat constant. Then
\displaystyle\frac{dT}{dt} = \displaystyle\frac{1380A - 2\sigma\epsilon A T^4}{mC}
\displaystyle\frac{mC}{A}\int\displaystyle\frac{1} {1380 - 2\sigma\epsilon T^4}dT = \int dt
I tried to integrate it on integrals.wolfram.com taking boltzmann constant as 5.6E-8 and emissivity as 0.7. The result was
\displaystyle\frac{0.156942mC}{A}(\arctan[0.00230862T]+arctanh[0.00230862T]) + C' = t
C' is here the integration constant
I dont know how to proceed further. Can anyone help please?
Thank you
I tried this.
Let A be the area exposed to the Sun and 2A the total area of the body. Let 1380 W/m2 be the power of the sunlight falling on the body. Let \sigma be the boltzmann constant, \epsilon the emissivity of the body and T the temperature at a a particular instant of time, m the mass of the body and C the specific heat constant. Then
\displaystyle\frac{dT}{dt} = \displaystyle\frac{1380A - 2\sigma\epsilon A T^4}{mC}
\displaystyle\frac{mC}{A}\int\displaystyle\frac{1} {1380 - 2\sigma\epsilon T^4}dT = \int dt
I tried to integrate it on integrals.wolfram.com taking boltzmann constant as 5.6E-8 and emissivity as 0.7. The result was
\displaystyle\frac{0.156942mC}{A}(\arctan[0.00230862T]+arctanh[0.00230862T]) + C' = t
C' is here the integration constant
I dont know how to proceed further. Can anyone help please?
Thank you