Question

A Styrofoam ice box has a total area of 0.950 m2and walls with an average thickness of 2.50 cm. The box contains ice, water, and canned beverages at 0ºC . The inside of the box is kept cold by melting ice. How much ice melts in one day if the ice box is kept in the trunk of a car at35.0ºC ?

Answer 1

Answer:

The mass of the ice is 3.44 kg.

Explanation:

Given that,

Area of ice box A= 0.950 m²

Thickness d= 2.50 cm

Temperature T₁= 0° C

Temperature T₂= 35.0°C

Time t = 1 day = 86400 s

We need to calculate the mass of ice

Using equation of rat of heat transfer by conduction

$\dfrac{Q}{t}=\dfrac{kA(T_{2}-T_{1})}{d}$

$\dfrac{Q}{t}=\dfrac{0.010\times0.950(35-0)}{2.50\times10^{-2}}$

$\dfrac{Q}{t}=13.3\ j/s$

The heat is used to melt the ice

$Q=mL_{f}$

$m=\dfrac{Q}{L_{f}}$....(I)

We need to calculate the heat

$Q = \dfrac{Q}{t}\times t$

$Q=13.3\times86400$

$Q=1149120=1.15\times10^{6}\ J$

Put the value of Q in the equation (I)

$m=\dfrac{1.15\times10^{6}}{334\times10^{3}}$

$m=3.44\ kg$

Hence, The mass of the ice is 3.44 kg.