To find the specific heat of the metal and determine its identity, we need to use the equation:
q = m × c × ΔT
where:
q = heat gained or lost by the system
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
First, let's find the heat gained or lost by the water using the equation:
q_water = m_water × c_water × ΔT_water
Given:
m_water = 150.50 g (mass of water)
c_water = 4.18 J/g·°C (specific heat capacity of water)
ΔT_water = T_final - T_initial = 31.4°C - 22.5°C = 8.9°C (change in water temperature)
Substituting the given values into the equation, we can calculate q_water:
q_water = 150.50 g × 4.18 J/g·°C × 8.9°C
Solving this equation gives us the value of q_water.
Now, let's find the heat gained or lost by the metal using the equation:
q_metal = m_metal × c_metal × ΔT_metal
Given:
m_metal = 225.0 g (mass of metal)
c_metal = ? (specific heat capacity of the metal)
ΔT_metal = T_final - T_initial = 31.4°C - 95.5°C = -64.1°C (change in metal temperature)
Since the metal is losing heat to the water, the change in temperature is negative. Substituting the given values into the equation, we have:
q_metal = 225.0 g × c_metal × -64.1°C
Now, we know that the heat gained by the water is equal to the heat lost by the metal (assuming no heat loss to the surroundings):
q_water = q_metal
Therefore, we can set up an equation equating the two:
150.50 g × 4.18 J/g·°C × 8.9°C = 225.0 g × c_metal × -64.1°C
Simplifying and solving for c_metal will give us the specific heat capacity of the metal.
Once we find the specific heat capacity of the metal, we can use reference tables or periodic tables to identify the metal based on its specific heat capacity.