How much heat (in joules) would be required to raise the temperature of 500 g of an aluminum sphere from 20° C to 720° C? [Specific Heat Capacity of Aluminium is 900 J/(kgK)]

CONCEPT:

• Specific heat or specific heat capacity of a body: The amount of heat energy required to raise the temperature of a unit mass of a body through 1° C (or K) is called the specific heat of the material of the body.
  • It is generally denoted by C.

Q = mC∆T              
Where Q = heat required, ∆T = change in temperature and m = mass of the body.
So specific heat capacity is,
\({\rm{C\;}} = {\rm{\;}}\frac{Q}{{mΔ T{\rm{\;}}\;}}\)

EXPLANATION:

Given - mass of aluminum sphere (m) = 500 g = 0.5 kg, T₁ = 20° C, and T₂ = 720° C

⇒ ΔT = T₂ - T₁ =  (720 - 20)° C = 700° C

• The amount of heat (in joules) required to raise the temperature of 500 g of an aluminum sphere is 

⇒ Q = mC∆T     

⇒ Q = 0.5 × 900 × 700

⇒ Q = 315000

⇒ Q = 3.15 × 10⁵ J