Question

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.

Answer 1

This question is incomplete, the complete question is;

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 ⇒ $q_{rad$ = σT⁴, where σ = 5.67 × 10⁻¹¹ kW/m².K⁴

b ⇒ $q"$ = $q_{flame$ -  $q_{rad$

c ⇒ $m"$ =  $q"$/L, where L = 1.6 kJ/g

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

Answer:

a) $q_{rad$ = 8.54 kW/m²

b) $q"$ = 23.46 kW/m²

c) $m"$ = 14.6625 g/m²

d) Q = 1095.2888 kJ

Explanation:

Given the data in the question;

$q_{flame$ = 32 kW/m²

Area; A = 3m²

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

Now,

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

we substitute

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

$q_{rad$ = ( 5.67 × 10⁻¹¹ kW/m².K⁴ ) × 150644120641 K⁴

$q_{rad$ = 8.54 kW/m²

b) ⇒ $q"$ = $q_{flame$ - $q_{rad$

we substitute

$q"$ = 32 kW/m² - 8.54 kW/m²

$q"$ = 23.46 kW/m²

c) ⇒ $m"$ =  $q"$/L, where L = 1.6 kJ/g

we substitute

$m"$ =  23.46 / 1.6

$m"$ = 14.6625 g/m²

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

we substitute

Q =  14.6625 × 3 × 24.9

Q = 1095.2888 kJ