Question

A 23.05 g of a metal alloy is heated to 100. °C in boiling water. The alloy is placed in 50.00 g of water at 20.0°C. The temperature of the water increases to 29.5°C. Determine the specific heat capacity of the alloy.​

Answer 1

The specific heat capacity of the metal alloy is calculated using the conservation of energy and the information provided. By equalizing the heat gained by the water to the heat lost by the metal and plugging in the known values, the specific heat capacity of the metal alloy is found to be approximately 1.243 J/g°C.

Step-by-step explanation:

To determine the specific heat capacity of the metal alloy, we use the concept of conservation of energy, assuming no heat loss to the surroundings. The heat gained by the water is equal to the heat lost by the metal:

Q_water = Q_metal

(m_water)(c_water)(ΔT_water) = (m_metal)(c_metal)(ΔT_metal)

Given that:

• m_water = 50.00 g
• c_water = 4.18 J/g°C (specific heat capacity of water)
• ΔT_water = 29.5°C - 20.0°C
• m_metal = 23.05 g
• ΔT_metal = 100.0°C - 29.5°C

Plugging in the values:

(50.00 g)(4.18 J/g°C)(9.5°C) = (23.05 g)(c_metal)(70.5°C)

After calculating the left side:

1971 J = (23.05 g)(c_metal)(70.5°C)

Now we solve for c_metal:

c_metal = 1971 J / ((23.05 g)(70.5°C))

c_metal ≈ 1.243 J/g°C

The specific heat capacity of the metal alloy is approximately 1.243 J/g°C.