Final answer:
The final temperature of the iron when 37500 J of heat are added to 500 g at 70°C is 236.67°C, calculated using the specific heat capacity and the formula q = mcΔT.
Step-by-step explanation:
To calculate the final temperature of iron when heat is added, we can use the formula: q = mcΔT, where q is the heat added in joules, m is the mass in grams, c is the specific heat capacity in J/(g°C), and ΔT is the change in temperature in degrees Celsius.
In this case, we know the mass of the iron (500 g), the initial temperature (70°C), the specific heat capacity of iron (cIron = 0.45 J/(g°C)), and the heat added (37500 J). We need to find the final temperature (Tfinal).
Rearranging the formula to solve for ΔT: ΔT = q / (mc), and then add the initial temperature to find Tfinal: Tfinal = Tinitial + ΔT.
First, calculate the temperature change using the heat added:
ΔT = q / (mc) = 37500 J / (500 g × 0.45 J/(g°C)) = 37500 J / (225 J/°C) = 166.67 °C
Then, determine the final temperature:
Tfinal = Tinitial + ΔT = 70°C + 166.67°C = 236.67°C
The final temperature of the iron will be 236.67°C.