Question

95.0 g of an unknown metal at 100∘C is placed in 800 g of water at 25.0∘C. The final temperature of the water is 29.8∘C. What was the specific heat of the metal?

a) [Your calculated value]
b) 0.5 J/g°C
c) 0.25 J/g°C
d) 0.05 J/g°C

Answer 1

To determine the specific heat of the metal, you can use the equation q_metal + q_water = 0 and solve for the unknown specific heat capacity of the metal. The identity of the metal can be determined by comparing the specific heat capacity value obtained with the known specific heat capacities of different metals.

Step-by-step explanation:

To find the specific heat of the metal, we can use the equation:

q_metal + q_water = 0

The heat gained by water is provided via:

q_water = m_water * C_water * ΔT

where m_water is the mass of water, C_water is its specific heat capacity, and ΔT is the temperature change of water.

The heat lost by the metal is given by:

q_metal = m_metal * C_metal * ΔT

where m_metal is the mass of the metal and C_metal is the specific heat capacity of the metal.

Solving the equation using the given values:

1. Calculate the heat gained by the water using the mass of water, the specific heat capacity of water, and the change in temperature of the water.
2. Calculate the heat lost by the metal using the mass of the metal, the unknown specific heat capacity of the metal, and the change in temperature of the metal.
3. Set the sum of the heat gained and lost equal to zero and solve for the unknown specific heat capacity of the metal.

The specific heat capacity of the metal can be determined using these calculations. The identity of the metal can then be determined by comparing the specific heat capacity value obtained with the known specific heat capacities of different metals.