Road to Keyblade Master

Classical Mechanics Level 3

In an training site, a Keyblade wielder is practing two types of spells: Firaga and Blizzaga. Firaga is a fire-element spell that releases a heat wave with heat quantity equal to +6000 cal. Blizzaga, on the other hand, is an ice-element spell that freezes the target with heat quantity equal to -40000 cal.

The Keyblade wielder has a new small challenge for him: he needs to heat up a $5 dm^{3}$ container of water from 10°C to 90°C (precisely). In order to do so, he has to hit the container with Firaga and Blizzaga several times. In order to cast Firaga, he spends 10 MP (Magic Points) and, to cast Blizzaga, 50 MP. By the end of the day, he was able to make it, spending 900 MP in total.

Consider that a is the amount of times he casted Firaga and b the amount of times he casted Blizzaga. What is a + b ?

Notes and assumptions:

The water's heat capacity is $c = 1 \frac{cal}{g \times °C}$

Water's density is $1 g/cm^{3}$

There is no energy loss in the process

Neglect the heat absorbed by the recipient

(This problem is based on the Video Games series Kingdom Hearts , owned by Square Enix and Disney Interactive Studios. I am not affiliated with any of these companies)

The answer is 82.

1 solution

Leonardo Scarton
Sep 11, 2015

First of all, calculate the mass of water: $d = \frac{m}{v}$ , where d is the density of water, m is tha mass and v is the volume. $5dm^{3} = 5000 cm^{3}$ , so the equation is $1 = \frac{m}{5000}$ ; $m = 5000g$ .

Now, calculate the heat quantity variation, using the formula $Q = m \times c \times \Delta T$ .

$Q = 5000 \times 1 \times (90 - 10)$

$Q = 400000 cal$

Now, we have that the number of calories given by Firaga subtracted by the number os calories taken by Blizzaga is 400000. Also we have that the total of MP is 900. So we have the equations:

$6000a - 40000b = 400000$

$10a + 50b = 900$

$6000a - 40000b = 400000$

$-6000a - 30000b = -540000$

$-70000b = -140000$

$b = 2$

$10a + 50 \times 2 = 900$

$10a = 800$

$a = 80$

$a + b = 80 + 2 = \boxed{82}$

Road to Keyblade Master

The answer is 82.

1 solution

0 pending reports