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
Alright odusinakabira — let's do this. The problem describes a calorimetry scenario where a hot metal block is placed into cooler water. We assume that the heat lost by the metal block is equal to the heat gained by the water, and no heat is lost to the surroundings. Given values: • Mass of metal block, m_m = 0.5 kg • Initial temperature of metal block, T_m,i = 100^ • Specific heat capacity of metal, c_m = 400 J kg^-1 K^-1 • Mass of water, m_w = 1.0 kg • Initial temperature of water, T_w,i = 20^ • Specific heat capacity of water, c_w = 4200 J kg^-1 K^-1 Let the final temperature of the mixture be T_f. Step 1: Write the formula for heat exchange. The heat lost by the metal block is equal to the heat gained by the water. Q_lost, metal = Q_gained, water m_m c_m (T_m,i - T_f) = m_w c_w (T_f - T_w,i) Step 2: Substitute the given values into the equation. (0.5 kg) (400 J kg^-1 K^-1) (100^ - T_f) = (1.0 kg) (4200 J kg^-1 K^-1) (T_f - 20^) Step 3: Simplify both sides of the equation. 200 (100 - T_f) = 4200 (T_f - 20) 20000 - 200 T_f = 4200 T_f - 84000 Step 4: Rearrange the equation to solve for T_f. 20000 + 84000 = 4200 T_f + 200 T_f 104000 = 4400 T_f Step 5: Calculate the final temperature T_f. T_f = (104000)/(4400) T_f = (1040)/(44) T_f = (260)/(11) T_f ≈ 23.64^ The final temperature of the mixture is approximately 23.64^. Send me the next one 📸