Question

Two substances, iron and sand, initially at different temperatures, come into contact and reach thermal equilibrium. the mass of iron is 24.3 g and its initial temperature is 67.4 ∘c . the mass of sand is 25.6 g and its initial temperature is 21.2 ∘c . what is the final temperature of both substances at thermal equilibrium? (the specific heat capacity of iron is 0.449 j/(g⋅∘c) ; the specific heat capacity of sand is 0.84 j/(g⋅∘c) .)

Answer 1

The final temperature at thermal equilibrium between iron and sand is found by equating the heat lost by the iron to the heat gained by the sand and solving for the final temperature using the specific heat capacity and initial temperatures of each substance.

Step-by-step explanation:

To find the final temperature when iron and sand reach thermal equilibrium, we apply the concept of heat transfer. The heat lost by the iron will equal the heat gained by the sand, assuming no heat is lost to the surroundings.

We use the formula q = mcΔT, where q is the heat absorbed or released, m is mass, c is specific heat capacity, and ΔT is the change in temperature. The equation for the iron is q_iron = m_iron × c_iron × (T_final - T_initial_iron), and for sand, q_sand = m_sand × c_sand × (T_final - T_initial_sand).

As the heat lost by iron equals heat gained by sand, we set these equations equal to each other and solve for the final temperature, T_final:

m_iron × c_iron × (T_final - T_initial_iron) = m_sand × c_sand × (T_final - T_initial_sand)

Substitute the given values: 24.3 g × 0.449 J/g°C × (T_final - 67.4°C) = 25.6 g × 0.84 J/g°C × (T_final - 21.2°C).

Solving for T_final gives us the final temperature both substances reach at thermal equilibrium.