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
Let's knock this out. 26. Step 1: State the principle of calorimetry. Heat lost by steam = Heat gained by water. We need to consider two phases for the steam: condensation and cooling of the condensed water. Let T_f be the final temperature. Step 2: Calculate the maximum heat that can be gained by the water to reach 100^. The initial temperature of water is 20^. If the final temperature is 100^, the change in temperature for water is T_w = 100^ - 20^ = 80^. Given: Mass of water (m_w) = 500 g = 0.5 kg Specific heat capacity of water (c_w) = 4200 J/kg K Heat gained by water (Q_gained, water) to reach 100^: Q_gained, water = m_w c_w T_w Q_gained, water = (0.5 kg) × (4200 J/kg K) × (80 K) Q_gained, water = 168000 J Step 3: Calculate the maximum heat that can be lost by the steam if all of it condenses and cools to 20^. This involves two parts: Heat lost by condensation of steam at 100^ to water at 100^ (Q_condense). Heat lost by the condensed water (originally steam) from 100^ to 20^ (Q_cool, steam). Given: Mass of steam (m_s) = 100 g = 0.1 kg Latent heat of vaporization (L_v) = 2.26 × 10^6 J/kg Heat lost by condensation: Q_condense = m_s L_v Q_condense = (0.1 kg) × (2.26 × 10^6 J/kg) Q_condense = 226000 J Step 4: Compare the heat values to determine the final temperature. The heat released by just the condensation of all the steam (226000 J) is greater than the heat required to raise the temperature of the water to 100^ (168000 J). This means that the water will reach 100^, and not all the steam will condense. The excess heat from the steam (if it were to cool further) is not absorbed by the water because the water itself reaches the boiling point of the steam. Therefore, the final temperature of the mixture will be 100^. To confirm, the mass of steam required to condense to bring the water to 100^ is: m_condensed = Q_gained, waterL_v = 168000 J2.26 × 10^6 J/kg ≈ 0.0743 kg = 74.3 g Since 74.3 g is less than the available 100 g of steam, the water will reach 100^, and some steam will remain uncondensed at 100^. The correct option is C. C. 100^ 27. Good insulators are materials that trap air, which is a poor conductor. Air is an excellent thermal insulator because its molecules are far apart, reducing the frequency of collisions needed for heat transfer by conduction. Many insulating materials, like fiberglass, foam, or wool, work by trapping pockets of air. The correct option is B. B. Trap air, which is a poor conductor What's next? 🤔