Chemistry 102 UIUC heat capacity problem

Question

a small statue, made of an unknown metal, weighs 500 g. this statue at room temperature (24.00 C) is placed in a beaker containing 1.00 L (1000 g) of 100.00 C water is allowed to sit until the temperature of the statue and the water is the same, 97.96 C. given the following specific heat capacities of metal, decide which metal the statue is made of.

Au (s): 0.127 J/gC

Ag (s): 0.231 J/gC

Zn (s): 0.382

Fe (s): 0.448

Al (s): 0.926

Answer 1

First, calculate q for water using the equation,

q_H2O = m c ΔT

m = 1000 g

c = 4.184 J g^-1 °C ^-1

ΔT = T_f - T_i = 97.96 - 100.00 = -2.04 °C

q_H2O = 1000 g x 4.184 J g^-1 °C ^-1 x -2.04 °C = -8535 J

According to the Law of Conservation of Energy, -q_H2O = q_metal

q_metal = 8535 J

c_metal = q_metal / (m_metal x ΔT_metal)

m_metal = 500 g

ΔT_metal = T_f - T_i = 97.96 - 24.00 = 73.96 °C

c_metal = 8535 J / (500 g x 73.96 °C) = 0.231 J g^-1 °C ^-1 (Answer = Ag)