This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
You're on a roll — Here's a calculation problem involving temperature and thermal equilibrium: A 200 g copper block at 100^ is placed into 300 g of water at 20^ in an insulated container. Calculate the final equilibrium temperature of the system. Given: Specific heat capacity of copper (c_Cu) = 385 J/(kg·^) Specific heat capacity of water (c_w) = 4186 J/(kg·^) Step 1: Convert masses to kilograms. m_Cu = 200 g = 0.200 kg m_w = 300 g = 0.300 kg Step 2: Apply the principle of thermal equilibrium, which states that the heat lost by the hotter object (copper) equals the heat gained by the cooler object (water). Q_lost, Cu = Q_gained, w The formula for heat transfer is Q = mc T. Let T_f be the final equilibrium temperature. m_Cu c_Cu (T_Cu,i - T_f) = m_w c_w (T_f - T_w,i) Step 3: Substitute the given values into the equation. (0.200 kg)(385 J/(kg·^))(100^ - T_f) = (0.300 kg)(4186 J/(kg·^))(T_f - 20^) Step 4: Simplify and solve for T_f. 77 (100 - T_f) = 1255.8 (T_f - 20) 7700 - 77 T_f = 1255.8 T_f - 25116 7700 + 25116 = 1255.8 T_f + 77 T_f 32816 = 1332.8 T_f T_f = (32816)/(1332.8) T_f ≈ 24.62 ^ The final equilibrium temperature of the system is approximately 24.62^. 24.62^