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

You have collected exactly 1600 aluminum cans for recycling, each with a mass of 14.2 g, the energy needed to melt the aluminum cans is 7.98·10⁷ J.

Step-by-step explanation:

To calculate the energy needed to melt the aluminum cans, we need to consider two processes: raising the temperature of the cans to the melting point, and then melting them. Let's break it down:

First, we need to calculate the energy required to raise the temperature of the cans to the melting point using the specific heat capacity formula: Q = mcΔT.

Q = (1600 cans) x (0.0142 kg/can) x (899 J/kg ·°C) x (660.4°C - 26.3°C).

Next, we need to calculate the energy required to melt the cans using the latent heat of fusion formula: Q = mL.

Q = (1600 cans) x (0.0142 kg/can) x (3.97 ·10⁵ J/kg).

Q = 7.98·10⁷ J.

Therefore the total energy required to melt the cans is 7.98·10⁷ J.

Answer 2

The heat requied is
`21.97* 10^(6)Joules`

Step-by-step 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* 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* 14.2* 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* S.Heat* (ΔTemp)\\\\q_(1)=22.72kg* 899J/kg* (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* L.heat\\\\q_(2)=22.72* 3.97* 10^(5)\\\\\therefore q_(2)=9.02MJ`

Thus the total heat required is

`q_(1)+q_(2)\\\\=12.95+9.02=21.97MJ`