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
Welcome back ⚜️Léxïç — missed you this week. Here are the solutions for the problems: 12. Determine the specific heat capacity of the metal. Step 1: Identify the given values and the principle of heat exchange. The heat lost by the metal is equal to the heat gained by the oil. For the metal: Mass, m_m = 40 kg Initial temperature, T_m,i = 600^ Final temperature, T_m,f = 40^ Specific heat capacity, c_m = ? For the oil: Mass, m_o = 300 kg Initial temperature, T_o,i = 25^ Final temperature, T_o,f = 40^ Specific heat capacity, c_o = 2100 J/kg·^ The principle is Q_lost, metal = Q_gained, oil. The formula for heat transfer is Q = mc T. Step 2: Calculate the temperature changes for both the metal and the oil. For the metal: T_m = T_m,i - T_m,f = 600^ - 40^ = 560^ For the oil: T_o = T_o,f - T_o,i = 40^ - 25^ = 15^ Step 3: Set up the heat balance equation and solve for c_m. m_m c_m T_m = m_o c_o T_o (40 kg) · c_m · (560^) = (300 kg) · (2100 J/kg·^) · (15^) 22400 · c_m = 9450000 c_m = (9450000)/(22400) c_m = 421.875 J/kg·^ The specific heat capacity of the metal is 421.875 J/kg·^. 13. How much water is frozen? Step 1: Identify the given values and the principle of heat exchange. The heat gained by the ice to warm up to 0^ is equal to the heat lost by the water as it freezes. For the ice: Mass, m_ice = 100 g = 0.1 kg Initial temperature, T_ice,i = -20^ Final temperature, T_ice,f = 0^ Specific heat capacity of ice, c_ice = 2302 J/kg·^ For the water: Initial temperature, T_water,i = 0^ Latent heat of fusion, L_f = 3.35 × 10^5 J/kg Mass of water frozen, m_frozen = ? The principle is Q_gained, ice = Q_lost, water. Step 2: Calculate the heat gained by the ice to warm from -20^ to 0^. Q_gained, ice = m_ice c_ice T_ice T_ice = T_ice,f - T_ice,i = 0^ - (-20^) = 20^ Q_gained, ice = (0.1 kg) · (2302 J/kg·^) · (20^) Q_gained, ice = 4604 J Step 3: Calculate the mass of water frozen using the heat gained by the ice. The heat lost by the water as it freezes is given by Q_lost, water = m_frozen L_f. Since Q_gained, ice = Q_lost, water: 4604 J = m_frozen · (3.35 × 10^5 J/kg) m_frozen = 4604 J3.35 × 10^5 J/kg m_frozen ≈ 0.013743 kg To express this in grams: m_frozen ≈ 0.013743 kg × 1000 g/kg ≈ 13.743 g The mass of water frozen is approximately 0.0137 kg. Drop the next question! 📸