Water at 15^ C is contained inside a closed, thermally insulated copper vessel. The temperature increases to 17^ C after the vessel is vigorously shaken for 15 minutes. The mass of the water is 200 g and the mass of the vessel is 100 g . The specific heat capacities of copper and water are 420 J kg ⁻¹ K ⁻¹ and 4200 J kg ⁻¹ K ⁻¹ , respectively. Ignore any thermal expansion. What is the increase in the internal energy

Step-by-step solution

The increase in the internal energy of the system is given by the total heat capacity of the system multiplied by the change in temperature. The change in temperature is T = 17^ C - 15^ C = 2 K . The total heat capacity of the system is the sum of the heat capacities of the water and the copper vessel: C = m_w c_w + m_c c_c Substituting the given values: C = (0.2 kg ) (4200 J kg ⁻¹ K ⁻¹) + (0.1 kg ) (420 J kg ⁻¹ K ⁻¹) C = 840 J K ⁻¹ + 42 J K ⁻¹ = 882 J K ⁻¹ The increase in internal energy is: U = C T U = 882 2 = 17