Icebergs in the North Atlantic present hazards to shipping, causing the length of shipping routes to increase by about 30 percent during the iceberg season. Attempts to destroy icebergs include planting explosives, bombing, torpedoing, shelling, ramming, and painting with lampblack. Suppose that direct melting of the iceberg, by placing heat sources in the ice, is tried. How much heat is required to melt 14 percent of a 2.40×105 metric-ton iceberg? One metric ton is equal to 103 kg. Assume that the iceberg is at 0°C. (Note: To appreciate the magnitude of this energy, compare your answer to the Hiroshima atomic bomb which had an energy equivalent to about 15,000 tons of TNT, representing an energy of about 6.0×1013 J.)

Convert 2.40 x 10^5 metric tons to grams. Then heat required is

q = mass x heat fusion
You have the mass, look up the heat of fusion of ice and do the calculation.

You can multiply your answer by 0.14 to obtain the energy required to melt just 14% of the iceberg.

To calculate the amount of heat required to melt a portion of the iceberg, you can use the formula:

Q = m * L

Where Q is the heat energy required, m is the mass of the portion to be melted, and L is the latent heat of fusion for ice.

First, let's calculate the mass of the portion to be melted. We know that the iceberg weighs 2.40×10^5 metric tons and we want to melt 14 percent of it.

Mass of the iceberg = 2.40×10^5 metric tons
Mass to be melted = 14% of the mass of the iceberg

Mass to be melted = (14/100) * (2.40×10^5) metric tons

Convert metric tons to kilograms:
1 metric ton = 10^3 kg

Mass to be melted = (14/100) * (2.40×10^5) * (10^3) kg

Now, let's calculate the heat energy required using the formula:

Q = m * L

We know that the latent heat of fusion for ice (L) is 3.34x10^5 J/kg.

Q = (mass to be melted) * (latent heat of fusion)

Substitute the values to calculate Q.

Q = [(14/100) * (2.40×10^5) * (10^3)] * [(3.34x10^5) J/kg]

Simplify the equation to get the value of Q.

Q = (0.14 * 2.40×10^5 * 10^3) * (3.34x10^5) J

Now you can calculate the multiplication using the scientific notation rules:

Q = [0.14 * (2.40 * 10^5) * (10^3)] * (3.34*10^5) J

Q = (0.14 * 2.40 * 3.34) * (10^5 * 10^3 * 10^5) J

Q = 1.48296 * (10^5 * 10^3 * 10^5) J

Q ≈ 1.48296 × 10^(5 + 3 + 5) J

Q ≈ 1.48296 × 10^(13) J

Therefore, the amount of heat required to melt 14 percent of a 2.40×10^5 metric-ton iceberg is approximately 1.48296 × 10^13 J.

Comparing this value to the energy equivalent of the Hiroshima atomic bomb, which is approximately 6.0×10^13 J, we can see that the heat required to melt the iceberg is roughly one-fourth the energy of the atomic bomb.