A sheet of gold weighing 11.4 g and at a temperature of 14.5°C is placed flat on a sheet of iron weighing 18.4 g and at a temperature of 55.4°C. What is the final temperature of the combined metals? Assume that no heat is lost to the surroundings.

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Mergus Mergus · Answer 1 · 2019-07-30T10:40:44+02:00

Answer:

The final temperature of the combined metals is 49.2314 °C

Explanation:

Heat gain by gold = Heat lost by iron

Thus,

[tex]m_{gold}\times C_{gold}\times (T_f-T_i)=-m_{iron}\times C_{iron}\times (T_f-T_i)[/tex]

Where, negative sign signifies heat loss

Or,

[tex]m_{gold}\times C_{gold}\times (T_f-T_i)=m_{iron}\times C_{iron}\times (T_i-T_f)[/tex]

For gold:

Mass = 11.4 g

Initial temperature = 14.5 °C

Specific heat of gold = 0.129 J/g°C

For iron:

Mass = 18.4 kg

Initial temperature = 55.4 °C

Specific heat of water = 0.450 J/g°C

So,

[tex]11.4\times 0.129\times (T_f-14.5)=18.4\times 0.450\times (55.4-T_f)[/tex]

[tex]1.4706\times (T_f-14.5)=8.28\times (55.4-T_f)[/tex]

[tex]1.4706\times T_f-1.4706\times 14.5=8.28\times 55.4-8.28\times T_f[/tex]

[tex]1.4706\times T_f-21.3237=458.712-8.28\times T_f[/tex]

[tex]1.4706\times T_f+8.28\times T_f=458.712+21.3237[/tex]

[tex]T_f=49.2314[/tex]

Thus,

The final temperature of the combined metals is 49.2314 °C