Question

A hot lump of 36.2 g of iron at an initial temperature of 62.0 °C is placed in 50.0 mL of H2O initially at 25.0 °C and allowed to reach thermal equilibrium. What is the final temperature of the iron and water given that the specific heat of iron is 0.449 J/(g·°C)? Assume no heat is lost to surroundings.

Answer 1

To determine the final temperature of iron and water at thermal equilibrium, we utilize the specific heat capacities and the principle of conservation of energy where heat lost by iron equals heat gained by water. The formula q = mcΔT is applied for both substances and solved for the final temperature.

Step-by-step explanation:

To find the final temperature of the iron and water upon reaching thermal equilibrium, we can set the heat lost by the hot iron equal to the heat gained by the cooler water. We use the specific heat of the substances and the formula q = mcΔT, where q represents heat energy, m is mass, c is specific heat capacity, and ΔT is the change in temperature.

For the iron (Fe), the heat lost is given by:

• qFe = mFe · cFe · (ΔTFe)

Since water's density is approximately 1 g/mL, we can assume 50.0 mL of water has a mass of 50.0 g, and for the water, the heat gained is:

• qH2O = mH2O · cH2O · (ΔTH2O)

By setting these two expressions equal (qFe = qH2O) and knowing that ΔT is Tfinal − Tinitial, we can solve for the final equilibrium temperature.

This question pertains to the principles of heat transfer and thermodynamics, which are key concepts in physics.

Answer 2

temperature of 62.0 °C is placed in 50.0 mL of H2O initially at 25.0 °C and allowed to reach thermal equilibrium