6.01 A piece of iron (C=0.449 J/g°C) and a piece of gold (C=0.128 J/g°C) have id

Question

6.01 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 two 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 two 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 to 498 K. C) Since the two metals have the same mass, the thermal energy contained in the iron and gold after reaching thermal equilibrium will be the same. D) Since the two 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.

Explanation / Answer

Iron is at higher temperature so it will lose some heat and gold will absorb that heat

The heat lost by iron = Mass X change in temperature X specific heat = Mass X (498-Tf) X 0.449

Heat gain by gold = Mass X change in temperature X specific heat = Mass X (Tf-298) X 0.128

Both will be equal

Mass X (498-Tf) X 0.449 = Mass X (Tf-298) X 0.128

223.602 - 0.449 Tf = 0.128 Tf - 38.144

Tf = 261.746 / 0.577 = 453.63 K

So correct answer is : Since the two 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

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