Question

A glass pan is used to bake 2-kg brownies (C = 3000 J/kg.C°) from 10°C to 98°C. Since the pan is
transparent, nearly all radiant heat will be absorbed by the brownies. a) If the total heat of radiation
available from a microwave oven is 481 W, how long the baking last (in minutes)? b) If the cylindrical
heating element of the oven has dimensions of D = 2 cm and L = 40 cm, what is the surface
temperature of the element (in °C)? (A = πDL)

Answer 1

Answer:

A glass pan is used to bake 2-kg brownies (C = 3000 J/kg.C°) from 10°C to 98°C. Since the pan is

transparent, nearly all radiant heat will be absorbed by the brownies. a) If the total heat of radiation

available from a microwave oven is 481 W, how long the baking last (in minutes)? b) If the cylindrical

heating element of the oven has dimensions of D = 2 cm and L = 40 cm, what is the surface

temperature of the element (in °C)? (A = πDL

Answer 2

Concept:

We need to utilize the formula, t = mcΔθ/P and P = σAT⁴ to determine the time and surface temperature respectively.

Given:

mass of brownies = 2kg

Specific heat = 3000 J/kg⁰C

Change in temperature = 98-10 = 88⁰C

Total heat of radiation, P = 481 W

Diameter = 2cm

Length = 40cm

Find:

(a) We need to determine the time for baking, t

(b) We need to determine the surface temperature of the element, T

Solution:

(a) The total heat of radiation is given as, P = 481 W

We have, t = Q/P  ----- equation 1

We know, Q = mcΔθ

Therefore, equation 1 becomes,

t = mcΔθ/P

t = (2×3000×88) / 481

t = 528000 / 481 sec'

We need the time in min, therefore,

t = 528000/ (481×60)

t = 18.29 min

(b) Area of heating element is calculated by the formula, A = πDL

where, D = 2cm, L = 40cm and π = 3.14

Therefore, A = 3.14×2×40

A = 251.2 cm² = 251.2×10^-4 m²

Now, total heat radiation is calculated by the formula-

P = σAT⁴ where P = total heat of radiation, σ = stefan's constant = 5.67×10^-8 W/m², T= surface temperature of element

Therefore, T⁴ = P/σA

T = (P/σA)^1/4

T = [481/ 5.67×10^-8×251.2×10^-4]^1/4

T = 0.7619 ×10³ K = 761.9 K

In celcius, T = 761.9 - 273

T = 488.9⁰C

Thus, (a) The time taken by the baking of brownies is 18.29min.

(b) The surface temperature of the element is 488.9⁰C.

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