A metal rod of length 5.0 m and mass 200 g is supplied with 4000 J of heat energy. The specific heat capacity of the metal is 500 J kg ⁻¹ K ⁻¹ and its coefficient of linear expansion is 1.2 10⁻⁵ K ⁻¹ . Assuming no heat is lost to the surroundings, what is the increase in the length of the rod?

Step-by-step solution

First, calculate the change in temperature of the rod using the calorimetry formula Q = mc T . Given: Q = 4000 J m = 200 g = 0.2 kg c = 500 J kg ⁻¹ K ⁻¹ T = Q mc = 4000 0.2 500 = 4000 100 = 40 K Next, calculate the increase in length using the linear expansion formula L = L₀ T . Given: L₀ = 5.0 m = 1.2 10⁻⁵ K ⁻¹ L = 5.0 1.2 10⁻⁵ 40 L = 240 10⁻⁵ m = 2.4 10⁻³ m Converting to millimeters: L = 2.4 mm Answer: 2.4 mm