Plexiglas, polymethylmethacrylate (PMMA), is often used as display windows and cases in art galleries and museums. If its flame imparts 32 kW/m^2 to the surface when it burns estimate the energy release rate of a 3 m^2 square sheet (one side). Assume its vaporization temperature is 350°C. Calculate with units, provide work.

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Plexiglas, polymethylmethacrylate (PMMA), is often used as display windows and cases in art galleries and museums. If its flame imparts 32 kW/m^2 to the surface when it burns estimate the energy release rate of a 3 m^2 square sheet (one side). Assume its vaporization temperature is 350°C. Calculate with units, provide work.

a ⇒ = σT⁴, where σ = 5.67 × 10⁻¹¹ kW/m².K⁴

b ⇒ = -  

c ⇒ =  /L, where L = 1.6 kJ/g

d ⇒ Q =   × A × ΔHc, where ΔHc is 24.9 kJ/g

a) = 8.54 kW/m²

b) = 23.46 kW/m²

c) = 14.6625 g/m²

d) Q = 1095.2888 kJ

Explanation:

Given the data in the question;

= 32 kW/m²

Area; A = 3m²

vaporization temperature; T = 350°C = ( 350 + 273 )K = 623 K

Now,

a) ⇒ = σT⁴, where σ = 5.67 × 10¹¹ kW/m².K⁴

we substitute

= ( 5.67 × 10⁻¹¹ kW/m².K⁴ ) × ( 623 K)⁴

= ( 5.67 × 10⁻¹¹ kW/m².K⁴ ) × 150644120641 K⁴

= 8.54 kW/m²

b) ⇒ = -

we substitute

= 32 kW/m² - 8.54 kW/m²

= 23.46 kW/m²

c) ⇒ =  /L, where L = 1.6 kJ/g

we substitute

=  23.46 / 1.6

= 14.6625 g/m²

d) ⇒ Q =   × A × ΔHc, where ΔHc is 24.9 kJ/g

we substitute

Q =  14.6625 × 3 × 24.9

Q = 1095.2888 kJ

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