Question

An ice box has a total area of 0.950m^2 wall thickness 2.50cm the box contain ice water and can beverages at 0'C. How much ice melts in 1 day if the ice box is kept in the trunk of the car at 35.0'C?

Answer 1

Answer on Question #64846-Physics-Other

An ice box has a total area of $A = 0.950m^2$ wall thickness $d = 2.50cm = 0.025m$ the box contain ice water and can beaverages at $T_1 = 0{}^\circ C$. How much ice melts in $t = 1$ day $= 24$ h $= 86400$ s if the ice box is kept in the trunk of the car at $T_2 = 35.0{}^\circ C$?

Solution

The rate of heat transfer:

$$\frac {Q}{t} = \frac {k A (T _ {2} - T _ {1})}{d}$$ $$\frac {Q}{t} = \frac {(0 . 0 1 0) (0 . 9 5 0) (3 5 - 0)}{0 . 0 2 5} = 1 3. 3 W.$$

The heat for melting the ice:

$$Q = m L.$$ $$m = \frac {Q}{L} = \frac {\left(\frac {Q}{t}\right) t}{L} = \frac {(1 3 . 3) (8 6 4 0 0)}{3 3 4 \cdot 1 0 ^ {3}} = 3. 4 4 k g.$$

Answer: 3.44 kg.

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