Thank you for visiting A certain mixture of reacting chemicals contained in a spherical tank generates heat at a rate of 168 746 9 W m 3 If the. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The estimated temperature drop across the wall of the spherical tank is approximately 4.13 °C.
The temperature drop across the wall of the spherical tank can be estimated using the formula for heat conduction through a cylindrical wall. The formula is given by:
ΔT = (Q * r) / (4πkL)
where:
ΔT is the temperature drop in °C,
Q is the heat generation rate per unit volume (168746.9 W m^−3),
r is the radius of the tank wall (average of inner and outer radii) in meters,
k is the thermal conductivity of the steel (18 W m^−1K^−1),
L is the thickness of the tank wall in meters.
To calculate the radius of the tank wall (r):
r = (99.5 cm + 100.2 cm) / 2
= 99.85 cm = 0.9985 m
Assuming the thickness of the tank wall (L) is negligible compared to the radius, we can use this simplified formula:
ΔT = (Q * r) / (4πk)
Substituting the given values into the formula, we have:
ΔT = (168746.9 * 0.9985) / (4π * 18)
Calculating the result:
ΔT = 466.84 / (4π * 18)
≈ 4.13 °C
Learn more about temperature here:
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