6) Calculate the internal energy change when 1 mole of iron is cooled from 45°C to 13°C (specific heat capacity of iron is 0.449 J/g K).

Answer 1

ΔU = m * C * ΔT, where m = mass (kg); C = specific heat; ΔT = temperature change

ΔT = 1 mol Fe * 55.845 g/mol * 0.449 J/(g*K) * ((45+273.15) - (13+273.15)) = 802 J

Heat is released --> -802 J

Answer 2

The internal energy change of a system is equal to the heat absorbed by the system minus the work done by the system, ΔE = q - w. In this case the iron loses heat as it is cooled and also does no work, so q is negative and work done is zero and ΔE = -q.

The heat lost is calculated by multiplying the specific heat of iron by the mass of one mole and the change in temperature. Since we already know the heat is negative, we can use the absolute value of the temperature change.

ΔE = -q = 0.449 J/gK x 55.85 g/mole x Ι 13 - 45 Ι K = -99.8 kJ/mole.