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
Here's another calculation problem on temperature and thermal equilibrium: A 150 g aluminum block at 150^ is submerged into 400 g of water at 25^ in an insulated calorimeter. Determine the final equilibrium temperature of the mixture. Given: Specific heat capacity of aluminum (c_Al) = 900 J/(kg·^) Specific heat capacity of water (c_w) = 4186 J/(kg·^) Step 1: Convert masses to kilograms. m_Al = 150 g = 0.150 kg m_w = 400 g = 0.400 kg Step 2: Apply the principle of thermal equilibrium, where the heat lost by the aluminum equals the heat gained by the water. Q_lost, Al = Q_gained, w Using the formula Q = mc T, let T_f be the final equilibrium temperature. m_Al c_Al (T_Al,i - T_f) = m_w c_w (T_f - T_w,i) Step 3: Substitute the given values into the equation. (0.150 kg)(900 J/(kg·^))(150^ - T_f) = (0.400 kg)(4186 J/(kg·^))(T_f - 25^) Step 4: Simplify and solve for T_f. 135 (150 - T_f) = 1674.4 (T_f - 25) 20250 - 135 T_f = 1674.4 T_f - 41860 20250 + 41860 = 1674.4 T_f + 135 T_f 62110 = 1809.4 T_f T_f = (62110)/(1809.4) T_f ≈ 34.33 ^ The final equilibrium temperature of the mixture is approximately 34.33^. 34.33^ Last free one today — make it count tomorrow, or type /upgrade for unlimited.