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
Another one ~Dorinda — let's solve it. Step 1: Convert the given masses from grams to kilograms. m_ice = 200 g = 0.2 kg m_water = 500 g = 0.5 kg Step 2: Calculate the heat required to melt the ice at 0^ to water at 0^. The formula for latent heat of fusion is Q = mL_f. Q_melt = m_ice × L_f Q_melt = 0.2 kg × 336,000 J/kg Q_melt = 67,200 J Step 3: Set up the heat balance equation. Assuming no heat loss, the heat lost by the hot water equals the heat gained by the ice (to melt) plus the heat gained by the melted ice (to raise its temperature to the final temperature, T_f). Heat lost by hot water = Heat gained by ice (melting) + Heat gained by melted ice (warming up) m_water c_w (T_initial\_water - T_f) = Q_melt + m_ice c_w (T_f - T_initial\_ice) Substitute the known values: 0.5 kg × 4,200 J/kg^ × (60^ - T_f) = 67,200 J + 0.2 kg × 4,200 J/kg^ × (T_f - 0^) Step 4: Solve the equation for T_f. 2,100 (60 - T_f) = 67,200 + 840 T_f 126,000 - 2,100 T_f = 67,200 + 840 T_f Rearrange the terms to solve for T_f: 126,000 - 67,200 = 840 T_f + 2,100 T_f 58,800 = 2,940 T_f T_f = (58,800)/(2,940) T_f = 20^ The final temperature of the mixture is 20^. Send me the next one 📸