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 how to determine the final temperature of the mixture: Step 1: List the given values and necessary constants. Given: • Mass of steam (m_s) = 0.1 kg • Initial temperature of steam (T_s,i) = 100 °C • Mass of water (m_w) = 2 kg • Initial temperature of water (T_w,i) = 20 °C • Mass of copper can (m_c) = 0.2 kg • Specific heat capacity of copper (c_c) = 400 J/kgK • Initial temperature of copper can (T_c,i) = 20 °C Assumed constants: • Specific heat capacity of water (c_w) = 4200 J/kgK • Specific latent heat of vaporization of steam (L_v) = 2.26 × 10^6 J/kg Let the final temperature of the mixture be T_f. Step 2: Calculate the heat lost by the steam. The steam first condenses at 100 °C and then the resulting water cools from 100 °C to T_f. Heat lost by condensation (Q_1) = m_s L_v Heat lost by cooling of condensed water (Q_2) = m_s c_w (100 - T_f) Total heat lost by steam (Q_lost): Q_lost = Q_1 + Q_2 Q_lost = (0.1 kg × 2.26 × 10^6 J/kg) + (0.1 kg × 4200 J/kgK × (100 - T_f) K) Q_lost = 226000 J + (42000 - 420 T_f) J Q_lost = (268000 - 420 T_f) J Step 3: Calculate the heat gained by the water and the copper can. The water and the copper can both heat up from 20 °C to T_f. Heat gained by water (Q_3) = m_w c_w (T_f - 20) Heat gained by copper can (Q_4) = m_c c_c (T_f - 20) Total heat gained (Q_gained): Q_gained = Q_3 + Q_4 Q_gained = (2 kg × 4200 J/kgK × (T_f - 20) K) + (0.2 kg × 400 J/kgK × (T_f - 20) K) Q_gained = (8400 (T_f - 20)) J + (80 (T_f - 20)) J Q_gained = (8400 T_f - 168000) J + (80 T_f - 1600) J Q_gained = (8480 T_f - 169600) J Step 4: Apply the principle of calorimetry. According to the principle of calorimetry, heat lost equals heat gained: Q_lost = Q_gained 268000 - 420 T_f = 8480 T_f - 169600 Rearrange the equation to solve for T_f: 268000 + 169600 = 8480 T_f + 420 T_f 437600 = 8900 T_f T_f = (437600)/(8900) T_f = 49.1685... °C Step 5: State the final temperature. Rounding to one decimal place: T_f ≈ 49.2 °C That's 2 down. 3 left today — send the next one.