A 19.5-g sample of a metal was heated to 61.67°C. When the metal was placed into 26.5 g of water in a calorimeter, the temperature of the water increased from 25.00°C to 30.00°C. What is the specific heat of the metal?
heat lost by metal + heat gained by H2O=0.
[mass metal x specific heat metal (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] = 0
Solve for specific heat metal, the only unknown..
To find the specific heat of the metal, we can use the equation:
q = m × c × ΔT
where q is the heat gained or lost by the substance, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
In this case, the water gained heat from the metal, so the heat gained by the water is equal to the heat lost by the metal. The heat gained by the water, q_water, can be calculated using the equation:
q_water = m_water × c_water × ΔT_water
where m_water is the mass of water and c_water is the specific heat capacity of water. We know the values of m_water (26.5 g), ΔT_water (ΔT_water = T_final - T_initial = 30.00°C - 25.00°C = 5.00°C), and c_water (4.18 J/g°C, which is the specific heat capacity of water).
q_water = (26.5 g) × (4.18 J/g°C) × (5.00°C)
q_water = 553.45 J
Since the heat lost by the metal is equal to the heat gained by the water:
q_metal = q_water
q_metal = 553.45 J
Now, we need to calculate the heat lost by the metal, q_metal. We can use the equation:
q_metal = m_metal × c_metal × ΔT_metal
where m_metal is the mass of the metal, c_metal is the specific heat capacity of the metal (which we want to find), and ΔT_metal is the change in temperature of the metal. We know the values of m_metal (19.5 g) and ΔT_metal (ΔT_metal = T_final - T_initial = 30.00°C - 61.67°C = -31.67°C).
q_metal = (19.5 g) × (c_metal) × (-31.67°C)
q_metal = -618.285 g·°C·c_metal
Since q_metal = q_water, we can set these two equations equal to each other and solve for c_metal:
-618.285 g·°C·c_metal = 553.45 J
Simplifying the equation:
c_metal = 553.45 J / (-618.285 g·°C)
Now, plug in the values and calculate:
c_metal = -0.895 J/g°C
Therefore, the specific heat of the metal is approximately -0.895 J/g°C.