Set 54 Problem number 12

Problem

It requires 169.33 Joules of energy to increase the temperature of 7 kg of a certain substance by 41 degrees Celsius. What is the specific heat of the substance? 

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 169.33 Joules to increase 7 kg by 41 Celsius, then thermal energy per kg required to raise to the given temperature is

• thermal energy per kg = ( 169.33 / 7) J/kg = 24.19 J/kg.

The per degree per Kg amount is thus

• thermal energy per kg and per degree: 24.19 J/Kg / ( 41 Celsius) = .59 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).