-You have a sample of unkonw metal that you have heated to 100 deg Celsius (oC) in boilin water. If, unknown to you, the metal sample cools somewhat before being added to your calorimeter, what will be the effect on the delta T for the water in your calorimeter (assume you have a "perfect" calorimeter)? How will this affect the calculated the specific heat of metal (cmetal)? How will this affect the caluclated molar mass of your metal sample?
If the sample is cooler wouldn't you expect delta T to be smaller; that is, the water in the calorimeter will not be heated as much and the final temperature will be smaller than it should be. Now plug that smaller T into the equation to obtain the answers to the other parts of the question.
If the unknown metal sample cools somewhat before being added to the calorimeter, it will lower the delta T (change in temperature) for the water in the calorimeter. This is because the initial temperature difference between the metal and the water would be reduced.
The effect on the calculated specific heat of the metal (cmetal) would depend on the extent of cooling. If the metal cools significantly before being added to the calorimeter, the temperature change of the water would be smaller, resulting in a lower calculated specific heat for the metal. On the other hand, if the cooling is minimal, the effect on the calculated specific heat would be negligible.
The calculated molar mass of the metal sample would not be affected by the cooling of the metal before being added to the calorimeter. The molar mass is determined based on the mass and moles of the metal, which are not dependent on the temperature change in the calorimeter. Therefore, the cooling of the metal sample would not impact the calculated molar mass.