Question

Question: How much heat, in joules and in calories, must be added to a 75.0–g iron block with a specific heat of 0.449 J/g °C to increase its temperature from 25 °C to its melting temperature of 1535 °C?

Short answer

The heat required to raise the temperature in joules = 50,849 J

The heat required to raise the temperature in calories = 12,147 calories

Step-by-step solution

Step 1: Specific heat

The heat required (Q) to raise the temperature of a substance is given by the formula Q = C × m ×∆ T,where “C” is the specific heat of the substance, “m” is the mass of the substance, and “∆T” is the change in the temperature of the substance.

Calculation of heat in Joules

We know from the given details that:

C = 0.449 J/g °C

m = 75 g

T = change in temperature =T_final - T_initial = 1535⁰C – 25⁰C = 1510⁰C

By putting the values above in the equation Q = C × m × ∆ T, we get:

Q = 75 × 0.449 × 1510 = 50,849 J.

The heat required to raise the temperature of 75 g of iron block = 50,849 J

Calculation of heat in calories

Also,

1 calorie = 4.184 J.

The heat required to raise the temperature in calories =\(\frac{{50,849}}{{4.186}} = 12147.39cal\)