A 0.145 kg mass of tungsten at 130.0 °C is placed in a 0.502 kg of water at 22.0 °C. The mixture reaches equilibrium at 28.6 °C. Calculate the specific heat of tungsten. (specific heat of water = 4180 J/kg C)
To calculate the specific heat of tungsten, we can use the principle of heat transfer. The heat gained (or lost) by an object can be calculated using the formula:
Q = mcΔT
where Q is the heat transferred, m is the mass of the object, c is the specific heat capacity of the material, and ΔT is the change in temperature.
In this case, we have a 0.145 kg mass of tungsten that is heated from 130.0 °C to 28.6 °C. We also know that the specific heat capacity of water (c) is 4180 J/kg°C.
First, let's calculate the heat gained by the water:
Q_water = (mass_water) * (specific heat capacity_water) * (change in temperature_water)
Q_water = (0.502 kg) * (4180 J/kg°C) * (28.6 °C - 22.0 °C)
Q_water = 0.502 kg * 4180 J/kg°C * 6.6 °C
Next, let's calculate the heat lost by the tungsten:
Q_tungsten = (mass_tungsten) * (specific heat capacity_tungsten) * (change in temperature_tungsten)
Q_tungsten = (0.145 kg) * (specific heat capacity_tungsten) * (28.6 °C - 130.0 °C)
The heat gained by the water is equal to the heat lost by the tungsten, so we can set up the equation:
Q_water = Q_tungsten
0.502 kg * 4180 J/kg°C * 6.6 °C = 0.145 kg * (specific heat capacity_tungsten) * (28.6 °C - 130.0 °C)
Now, we can solve for the specific heat capacity of tungsten by rearranging the formula:
(specific heat capacity_tungsten) = (0.502 kg * 4180 J/kg°C * 6.6 °C) / (0.145 kg * (28.6 °C - 130.0 °C))
After performing the calculations, we find that the specific heat capacity of tungsten is approximately 134 J/kg°C.