We have a piece of iron metal at 498 K and a piece of gold metal at 298 K and we need to determine whether the final temperature of both metal will be closer to the temperature of iron or gold.

When two substances at different temperatures are in contact with each other, heat flows from the one with higher temperature to the one with lower temperature.

A thermal equilibrium is achieved and the final temperature of both substances is equal.

**To solve this problem, we will find the final temperature of the system.**

Iron is at higher temperature therefore, heat will flow from iron to gold.

Since no heat is lost to the surroundings, all of the heat lost by iron will be gained by gold.

$\overline{){\mathbf{-}}{{\mathbf{q}}}_{{\mathbf{iron}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{{\mathbf{q}}}_{{\mathbf{gold}}}}$

Negative sign signifies the loss of heat.

A piece of iron (C = 0.449 J/g°C) and a piece of gold (C = 0.128 J/g°C) have identical masses. If the iron has an initial temperature of 498 K and the gold has an initial temperature of 298 K, which of the following statements is TRUE of the outcome when the two metals are placed in contact with one another? Assume no heat is lost to the surroundings.

a. Since the metals have the same mass, the final temperature of the two metals will be 398 K, exactly half way in between the two initial temperatures.

b. Since the metals have the same mass, but the specific heat capacity of gold is much smaller than that of iron, the final temperature of the two metals will be closer to 298 K than 498 K.

c. Since the metals have the mass, the thermal energy contained in the iron and gold after reaching thermal equilibrium will be the same.

d. Since the metals have the same mass, but the specific heat capacity of iron is much greater than that of gold, the final temperature of the two metals will be closer to 498 K than to 298 K.

e. None of the above are true

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