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

Step-by-step 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