The leftmost bath has a temperature of 144 degrees Celsius and is connected to t

Question

The leftmost bath has a temperature of 144 degrees Celsius and is connected to the middle bath by a cylindrical tube of radius 17.5 cm and length 14.5 cm

The middle bath has a temperature of 278 degrees Celsius and is additionally connected to the rightmost bath by a cylindrical tube of radius 17.1 cm and length 12.6 cm

The rightmost bath has a temperature of 297 degrees Celsius and is connected to the middle bath by the aforementioned tube.

Determine, in W, the amount of thermal power that is currently leaving or entering the middle bath.

Use a positive sign to denote an increase in thermal energy and a negative sign to denote a loss of thermal energy. Assume that all temperature gradients between baths are constant and the system is isolated from the surrounding environment.

Explanation / Answer

given Kspace = 0.6 W m-1 k-1   

TL = 144oC

Tm = 278oC

Tr = 297oC

RL = 17.5 cm = 0.175 m

and length LL = 14.5 cm = 0.145 m

radius 17.1 cm = Rr = 0.171 m

Lr = 12.4 cm = 0.124 m

using equation

H = K ( 3.14 X RL2 ( TL - Tm / LL ) - 3.14 X Rr2 ( Tm - Tr / Lr ) )

H = 0.6 ( 3.14 X 0.1752 ( 144 - 278 / 0.145 ) - 3.14 X 0.1712 ( 278 - 297 / 0.124 ) )

H = 0.6 X ( - 88.86 + 14.068 )

H = - 44.87 W

- ve sign (loss) indicates thermal power leaving from the middle bath

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