Steel balls 12 mm in diameter are annealed by heating to 1150 K and then slowly cooling to 400 K in an air environment for which T[infinity]=325 K and h=200 W/m2⋅K. Assuming the properties of the steel to be k=40 W/m⋅K, rho=7800 kg/m3, and c=600 J/kg⋅K, estimate the time required for the cooling process.

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13-12-2022
Physics

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Steel balls 12 mm in diameter are annealed by heating to 1150 K and then slowly cooling to 400 K in an air environment for which T[infinity]=325 K and h=200 W/m2⋅K. Assuming the properties of the steel to be k=40 W/m⋅K, rho=7800 kg/m3, and c=600 J/kg⋅K, estimate the time required for the cooling process.

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NomulaHarsh NomulaHarsh · Answer 1 · 2022-12-17T15:16:00+01:00

The estimated time required for cooling process is 2min.

What is specific heat?

Specific heat is a thermodynamic property that measures the amount of energy needed to raise the temperature of an object by a certain amount. It is measured in Joules per gram Celsius (J/(g.°C)). Specific heat is important in the study of thermodynamics because it allows us to calculate the amount of energy needed to change the temperature of a substance.

Given: initial temperature and diameter

Assumption: Negligible radiation effects

Solution: Lc=ro/3

Bi=hLc/k => h(ro/3)/k

=> 200 W/m2 x K(0.002m)/ 40 W/m⋅K

=>0.01

This shows that temperature of the steel remained nearly steady during cooling process.

using Lumped Capacitance method

t= (rho V cp/hAs ). ㏑Ti-T∞/T-T∞

=>( rho(πD³/6)cp / hπD²).㏑Ti-T∞/T-T∞

=>((7800 kg/m3(0.012m)600 J/kg⋅K) / 6x200 W/m2⋅K)ln 1150-325/400-325

t=>111.85s=1.82==2min

In the case of transient heat conduction, lumped capacitance method is used.

when a body with an initial temperature of Ti is abruptly placed on fluid with a temperature of T∞.

To learn more about specific heat visit given link:

https://brainly.com/question/27991746

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