Question

The murder weapon weighs 150 grams. The initial temperature of the weapon before being tested was 100 oC. After placing the weapon in the water, the temperature dropped to 25.13 oC. Find the specific heat capacity of the unknown metal by first calculating the heat energy gained by the water.
Water

Mass = 2500 g
Initial temperature = 25 o C Final temperature = 25.13 oC
Equations
q = m C p Δ T C p = q / (mΔT)

1. How much heat energy (q) did the water gain?

2. What is the specific heat capacity (C p) of the unknown metal?

3. Compare the heat capacity you calculated with the one below, which one matches?
Specific heat capacity of metal (J / g or C)
Silver 0.235

Gold 0.129 Lead 0.121
Copper

4. What metal was the murder weapon made of?
0.385

Answer 1

1. heat gained : 1358.5 J

2. Cp metal = 0.121 J/g C

3/4 The metal = Lead

Further explanation  

The law of conservation of energy can be applied to heat changes, i.e. the heat received/absorbed is the same as the heat released  

Q in = Q out  

Heat can be calculated using the formula:  

Q = mc∆T  

Q water(gained) = Q metal  (lost)

1. Heat of water gained

$\tt Q=2500\times 4.18\times (25.13-25)=1358.5~J$

2. The specific heat capacity (C p) of the unknown metal :

$\tt Cp=\dfrac{1358.5}{150\times (100-25.13)}=0.121~J/g^oC$