Question

Enter your answer in the provided box. A sheet of gold weighing 10.2 g and at a temperature of 19.4°C is placed flat on a sheet of iron weighing 19.9 g and at a temperature of 50.8°C. What is the final temperature of the combined metals?

Answer 1

46.73ºC

Step-by-step explanation:

The sheets will change heat to achieve the thermal equilibrium, it means that they'll have the same final temperature (T). The heat (q) must be equal for both in magnitude, but with opposite directions.

The heat flows from the higher temperature for the lower, so it flows from the iron (Fe) to the gold (Au) sheet:

qAu = -qFe

The heat can be calculated by the equation:

q = m*cp*ΔT

Where m is the mass, cp is the specif heat capacity, and ΔT the temperature variation.

CpAu = 0.129 J/gºC

CpFe = 0.444 J/gºC

10.2*0.129*(T - 19.4) = -19.9*0.444*(T - 50.8)

1.3158*(T - 19.4) = -8.8356*(T - 50.8)

1.3158T - 25.52652 = -8.8356T + 448.84848

1.3158T + 8.8356T = 448.84848 + 25.52652

10.1514T = 474.375

T = 46.73ºC