Two solid spheres, A and B, are made of different materials. The ratio of the density of A to that of B is 3 : 1 , the ratio of their specific heat capacities is 2 : 1 , and the ratio of their coefficients of linear expansion is 5 : 1 . If the same amount of heat is supplied to both spheres, the ratio of the change in volume of sphere A to the change in volume of sphere B is :

Step-by-step solution

The change in volume of a solid is given by: V = V₀ T = V₀ (3 ) T The rise in temperature when heat Q is supplied is: T = Q m c Since mass m = V₀ , we can substitute this into the temperature equation: T = Q V₀ c Substituting T back into the volume expansion equation: V = V₀ (3 ) ( Q V₀ c ) = 3 Q c Notice that the initial volume V₀ cancels out. Since the same amount of heat Q is supplied to both spheres, the change in volume is proportional to c . Therefore, the ratio of the changes in volume is: V_A V_B = ( _A _B