Final answer:
To calculate the energy needed to decrease the temperature of 4 kg of iron from 12 °C to -34 °C, use the formula q = mcΔT, where ΔT is the temperature change. The energy required is -71,280 J, with the negative sign indicating heat removal.
Step-by-step explanation:
To calculate the energy needed to be transferred to decrease the temperature of 4 kg of iron with a specific heat capacity of 390 J/kg °C from 12 °C to -34 °C, we use the formula:
q = mcΔT,
where q is the heat transfer, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
First, we calculate the change in temperature (ΔT):
ΔT = T_final - T_initial = -34 °C - 12 °C = -46 °C.
Then, we plug the values into the heat transfer equation:
q = (4 kg) · (390 J/kg °C) · (-46 °C) = -71,280 J.
The negative sign indicates that heat is being removed from the iron.