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
