Question

You have collected exactly 1600 aluminum cans for recycling, each with a mass of 14.2 g. How much energy is needed to melt them if their initial temperature is 26.3â¦C? Assume the specific heat, the latent heat and the melting point of aluminum are 899 J/kg ·⦠C,

3.97 à 105 J/kg and 660.4 â¦C, respectively. Answer in units of J.

Answer 1

Answer:

The heat requied is $21.97\times 10^{6}Joules$

Explanation:

According to the given data

1) Initial temperature of can = $26.3^{o}C$

2) Specific Heat of Aluminum can = $899J/kg$

3) Latent Heat of Aluminum can = $3.97\times 10^{5}J/kg/^{o}C$

4) Melting point of of Aluminum can = $660.4^{o}C$

5) Toatl mass of of Aluminum can = $1600\times 14.2\times 10^{-3}=22.72kg$

Now in order to melt the can we first need to raise it's temperature from $26.3^{o}C$ to $660.4^{o}C$

Thus the ensergy required is calculated as

$q_{1}=mass\times S.Heat\times (ΔTemp)\\\\q_{1}=22.72kg\times 899J/kg\times (660.4-26.3)\\\\\therefore q_{1}=12.95MJ$

Now the heat required to change the phase from solid aluminum to liquid phase can be calculated as

$q_{2}=mass\times L.heat\\\\q_{2}=22.72\times 3.97\times 10^{5}\\\\\therefore q_{2}=9.02MJ$

Thus the total heat required is

$q_{1}+q_{2}\\\\=12.95+9.02=21.97MJ$