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Korolek [52]
3 years ago
12

An electric furnace is to melt 40 kg of aluminium/hour. The initial temperature of aluminium is 32°C. Given that aluminium has s

pecific heat capacity 950 J/kg K melting point 680*C, latent heat of fusion 450 kJ/kg, the efficiency of furnace is 85% and cost of energy is 20 cents/kWhr Calculate: (a) Power required (b) The cost of operating the furnace for 30 hours
Physics
1 answer:
gizmo_the_mogwai [7]3 years ago
3 0

Answer:

Part a)

P = 13.93 kW

Part b)

R = 8357.6 Cents

Explanation:

Part A)

heat required to melt the aluminium is given by

Q = ms\Delta T + mL

here we have

Q = 40(950)(680 - 32) + 40(450 \times 10^3)

Q = 24624 kJ + 18000 kJ

Q = 42624 kJ

Since this is the amount of aluminium per hour

so power required to melt is given by

P = \frac{Q}{t}

P = \frac{42624}{3600} kW

P = 11.84 kW

Since the efficiency is 85% so actual power required will be

P = \frac{11.84}{0.85} = 13.93 kW

Part B)

Total energy consumed by the furnace for 30 hours

Energy = power \times time

Energy = 13.93 kW\times 30 h

Energy = 417.9 kWh

now the total cost of energy consumption is given as

R = P \times 20 \frac{Cents}{kWh}

R = 417.9 kWh\times  20 \frac{cents}{kWh}

R = 8357.6 Cents

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