Set 54 Problem number 12

Problem

What is the specific heat of a substance if it requires 191.52 Joules of energy to increase the temperature of 16 kg of the substance by 21 degrees Celsius?

Solution

Specific heat is the amount of thermal energy, per degree per unit of mass, required to raise the temperature of an object.

If it requires 191.52 Joules to increase 16 kg by 21 Celsius, then thermal energy per kg required to raise to the given temperature is

• thermal energy per kg = ( 191.52 / 16) J/kg = 11.97 J/kg.

The per degree per Kg amount is thus

• thermal energy per kg and per degree: 11.97 J/Kg / ( 21 Celsius) = .57 J/(Kg Celsius),

which is the specific heat (the thermal energy capacity per standard unit).

Generalized Solution

If thermal energy `dQ is required to increase the temperature of mass m of a substance by `dT degrees, then the thermal energy per degree is `dQ / `dT, and the thermal energy per degree, per unit of mass is

specific heat = c = `dQ / (m `dT).