How much heat is required to melt 200 kg of steel with a temperature of 1000 degrees Celsius?

Given:

m = 200 kilograms is the mass of steel;

T1 = 1000 degrees Celsius – initial steel temperature;

T = 1300 degrees Celsius – steel melting temperature;

c = 550 J / (kg * C) – specific heat capacity of steel;

q = 78 * 10 ^ 3 J / kg – specific heat of melting of steel.

It is required to determine Q (J) – the amount of heat required to melt steel mass m.

Let’s find the amount of heat for heating steel to the melting point:

Q1 = c * m * (T – T1) = 550 * 200 * (1300 – 1000) = 550 * 200 * 300 =

= 110,000 * 300 = 33,000,000 Joules = 33 * 10 ^ 6 Joules.

Let’s find the amount of heat required to melt steel:

Q2 = q * m = 78 * 10 ^ 3 * 200 = 15,600 * 10 ^ 3 = 15.6 * 10 ^ 6 Joules.

Then:

Q = Q1 + Q2 = 33 * 10 ^ 6 + 15.6 * 10 ^ 6 = 48.6 * 10 ^ 6 Joules = 48.6 MJ.

Answer: to melt steel, you need an amount of heat equal to 48.6 MJ.