Question

A sample of metal with a specific heat capacity of 0.50 kj kg ◦c is heated to 98◦c and then placed in an 0.055 kg sample of water at 22◦c. when equilibrium is reached, the final temperature is 35◦c. what was the mass of the metal?

Answer 1

The mass of the metal is determined by equalizing the heat lost by the metal to the heat gained by the water when they reach thermal equilibrium, applying the heat transfer formula, and solving for the mass of the metal.

Step-by-step explanation:

To determine the mass of the metal using the principle of conservation of energy, we will use the fact that the heat lost by the metal will be equal to the heat gained by the water when they reach thermal equilibrium. We use the formula:

Qmetal = Qwater

where Q is the heat transfer, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. The formula for heat transfer Q is m * c * ΔT.

For water, we use its specific heat capacity (cwater = 4.18 kJ/kg°C), and for the metal, it is given as 0.50 kJ/kg°C.

Let's denote mmetal as the mass of the metal we're trying to find. The final temperature (both the metal and water reach) is 35°C, so the change in temperature for the metal and water are:

• 
  
• ΔTmetal = 98°C - 35°C = 63°C
• 
  
• ΔTwater = 35°C - 22°C = 13°C

Using the heat transfer formula, we have:

mmetal * 0.50 kJ/kg°C * 63°C = 0.055 kg * 4.18 kJ/kg°C * 13°C

By solving for mmetal:

mmetal = (0.055 kg * 4.18 kJ/kg°C * 13°C) / (0.50 kJ/kg°C * 63°C)

After calculating, we find the mass of the metal.