Answer: 5.1 x 10^5 cal
Step-by-step explanation:
Given that the question asks to calculate the energy needed to increase the temperature of the Valyrian steel dagger, this is a specific heat capacity problem. We can use the formula q=mCΔT to solve for q, the energy needed to create a change in temperature (ΔT) of 120°C. We are given the mass of the dagger (m=39.0 g) and the material's specific heat (456 J/g°C):
q = (39.0 g) * ( 456 J/g°C) * 120°C = 2134080 J (2 significant figures)
The units of gram and celsius cancel out, leaving us with joules. However, the question wants the energy to be expressed as calories (cal). The conversion factor is 1 cal = 4.184 J. Therefore, our final answer is:
2134080 J (1 cal/4.184 J) = 510057.3614 cal (2 significant figures).
Using significant figure rules and scientific notation, the final answer can be represented as: 5.1 x 10^5 cal.