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A sheet of gold weighing 12.0 g with an initial temperature of 15 °C is placed flat on a 20.0g plate of iron that has been heated to 55°C. What is the final temperature of both pieces of metal? The specific heat of iron is 0.449 J/g°C and the specific heat of gold is 0.129 J/g°C.

Respuesta :

Answer:

49.12 °C

Explanation:

[tex]m_{g}[/tex] = mass of gold sheet = 12 g

[tex]c_{g}[/tex] = specific heat of gold = 0.129 J/g°C

[tex]T_{gi}[/tex] = initial temperature of gold sheet = 15 °C

[tex]m_{i}[/tex] = mass of iron sheet = 20 g

[tex]c_{i}[/tex] = specific heat of iron = 0.449 J/g°C

[tex]T_{ii}[/tex] = initial temperature of iron sheet = 55 °C

[tex]T_{f}[/tex] = Final equilibrium temperature

Using conservation of heat

[tex]m_{g} c_{g} (T_{f} - T_{gi}) = m_{i} c_{i} (T_{ii} - T_{f} ) \\(12)(0.129)(T_{f} - 15) = (20)(0.449)(55 - T_{f})\\(1.548) (T_{f} - 15) = (8.98) (55 - T_{f})\\T_{f} = 49.12 C[/tex]

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