A mass of 0.200 kg of an unknown metal at 94C is placed in 0.3 kg of water at 10C. The final temperature of the metal and water are 20C. What is the specific heat capacity of the unknown metal?
To find the specific heat capacity of the unknown metal, we can use the principle of conservation of energy. The heat lost by the metal is equal to the heat gained by the water.
First, let's calculate the heat lost by the metal. We can use the formula:
Q = mcΔT
Where:
Q is the heat lost (or gained),
m is the mass,
c is the specific heat capacity,
ΔT is the change in temperature.
Given:
m (mass of the unknown metal) = 0.200 kg
ΔT (change in temperature of the metal) = 94°C - 20°C = 74°C
Assuming the specific heat capacity of water is 4.18 J/g°C, we can calculate the heat lost by the metal:
Q = (0.200 kg) c (specific heat capacity of the metal) (74°C)
Next, let's calculate the heat gained by the water. Again, we'll use the formula:
Q = mcΔT
Given:
m (mass of the water) = 0.3 kg
c (specific heat capacity of water) = 4.18 J/g°C
ΔT (change in temperature of the water) = 20°C - 10°C = 10°C
Q = (0.3 kg) (4.18 J/g°C) (10°C)
Since the heat lost by the metal is equal to the heat gained by the water, we can set up an equation:
(0.200 kg) c (74°C) = (0.3 kg) (4.18 J/g°C) (10°C)
Simplifying the equation:
0.200 kg c (74°C) = 1.254 J/g
Now, we can solve for c, the specific heat capacity of the unknown metal:
c = (1.254 J/g) / (0.200 kg * 74°C)
c ≈ 0.089 J/g°C
Therefore, the specific heat capacity of the unknown metal is approximately 0.089 J/g°C.