A solid metallic object is heated by supplying 4 10^5 J of heat energy. The density of the metal is 8000 kg/m ^3 , its specific heat capacity is 500 J/(kg K) , and its coefficient of linear expansion is 2.0 10⁻⁵ K ⁻¹ . The increase in the volume of the object is:

Step-by-step solution

The heat energy Q supplied to the object is given by: Q = mc T where m is the mass, c is the specific heat capacity, and T is the increase in temperature. The mass of the object can be written in terms of its initial volume V₀ and density as m = V₀ . Substituting this into the heat equation: Q = V₀ c T V₀ T = Q c The increase in volume V is given by: V = V₀ T where is the coefficient of volume expansion. For an isotropic solid, = 3 . Substituting and V₀ T into the equation for V : V = (3 ) ( Q c ) Now, substituting