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maw [93]
3 years ago
8

A 0.250-kg aluminum bowl holding 0.800 kg of soup at 27.6°C is placed in a freezer. What is the final temperature if 424 kJ of e

nergy is transferred from the bowl and soup? Assume the soup has the same thermal properties as that of water, the specific heat of the liquid soup is 1.00 kcal/(kg · °C), frozen soup is 0.500 kcal/(kg · °C), and the latent heat of fusion is 79.8 kcal/kg. The specific heat of aluminum is 0.215 kcal/(kg · °C).
Physics
1 answer:
erastovalidia [21]3 years ago
4 0

Answer:

16.32 °C

Explanation:

We are given;

Mass of aluminum bowl; m_b = 0.25 kg

Mass of soup; m_s = 0.8 kg

Thus, formula to find the amount of heat energy for a temperature change of 27.6°C to 0°C is;

Q = (m_b•c_b•Δt) + (m_s•c_s•Δt)

Where;

c_b = 0.215 kcal/(kg•°C)

c_s = 1 kcal/(kg•°C)

ΔT = 27.6 - 0 = 27.6°C

Thus;

Q = (0.25 × 0.215 × 27.6) + (0.8 × 1 × 27.6)

Q = 23.5635 Kcal

Now, the energy that exits to be used to freeze the soup is;

Q' = 424 kJ - Q

Let's convert 424 KJ to Kcal

424 KJ = 424/4.184 Kcal = 101.3384 Kcal

Thus;

Q' = 101.3384 - 23.5635

Q' = 77.7749 Kcal

Amount of heat that's removed is given by;

Q_f = Q' - mL

Where;

m = m_s = 0.8 kg

L = 79.8 kcal/kg

Thus;

Q_f = 77.7749 - (0.8 × 79.8)

Q_f = 13.9349 Kcal

Then final temperature will be;

T_f = Q_f/((m_b•c_b) + (m_s•c_s))

T_f = 13.9349/((0.25 × 0.215) + (0.8 × 1))

T_f = 16.32 °C

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