Question

(a) A pair of students found a 3.0% error in Part A. They now have to distinguish between Cu (specific heat = 0.384 J/g · °C) or Zn (s = 0.389 J/g · °C). They have exactly 5.00 g of the metal.

What is the percent difference between the specific heats of the two metals? Use the specific heat of Cu as the theoretical value.
%

(b) Can they use calorimetry to determine which metal they have?

No

It depends on how hot the metal is before it is added it to the calorimeter.  

  This cannot be determined with the information given.

It depends on the amount of water used in the calorimeter.

Yes

Answer 1

a. Percent difference between the specific heats of the two metals

     = (0.389 - 0.384/0.384) x 100%

     = 1.3%

b. This cannot be determined with the information given. You need to know the initial and final temperature of the metal.

Explanation: Let the metal is Cu. To determine the specific heat of Cu in calorimetry you need to know the initial and final temperature of it.

Imagine an experiment in which a hot copper ball is dropped into a calorimeter containing water at room temperature. The copper ball will lose heat, which will be absorbed by the calorimeter and water. Because no heat enters or leaves the system, the heat balance for this experiment is ...

0 = q = q_Cu + q_cal + q_w

In this case q_Cu < 0, because the copper ball will lose heat to the calorimeter and water. Similarly q_cal > 0 and q_w > 0, because both the calorimeter and the water will gain heat.

In this experiment, all substances have the same final temperature (T_f), but not all substances have the same initial temperature. The copper ball is initially at temperature T_Cu while the calorimeter and water are initially at temperature T_i.

q_Cu = m_Cu s_Cu( T_f - T_Cu)

q_cal = C_cal( T_f - T_i)

q_w = m_w s_w( T_f - T_i)

From the above equations we get,

s_Cu = - (C_cal + m_w s_w) (T_f - T_i) / m_Cu(T_f - T_Cu)