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. Calculate the work that has been done on thi

Step-by-step solution

According to the first law of thermodynamics, U = Q + W . Since the vessel is thermally insulated, Q = 0 , which gives W = U . The change in internal energy of the system is the sum of the changes in internal energy of the water and the copper vessel: U = m_w c_w T + m_c c_c T Substituting the given values: m_w = 0.2 kg , c_w = 4200 J kg ⁻¹ K ⁻¹ m_c = 0.1 kg , c_c = 420 J kg ⁻¹ K ⁻¹ T = 17^ C - 15^ C = 2 K W = (0.2 4200 + 0.1 420) 2 W = (840 + 42) 2 W = 882 2 = 1764 J