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.
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b) Calculate the value of the atmospheric pressure? Step 1: Identify the initial and final states of the air column. In Figure (a) (tube upright): Length of air column, L_1 = 26 cm Length of mercury thread, h = 5 cm The pressure of the trapped air is the atmospheric pressure plus the pressure due to the mercury column: P_1 = P_atm + h = P_atm + 5 cmHg In Figure (b) (tube inverted): Length of air column, L_2 = 30 cm Length of mercury thread, h = 5 cm The pressure of the trapped air is the atmospheric pressure minus the pressure due to the mercury column: P_2 = P_atm - h = P_atm - 5 cmHg Step 2: Apply Boyle's Law. Assuming the temperature remains constant, Boyle's Law states P_1V_1 = P_2V_2. Since the tube has a uniform cross-sectional area A, the volume of the air column is V = LA. So, P_1L_1A = P_2L_2A, which simplifies to P_1L_1 = P_2L_2. Step 3: Substitute the expressions for pressure and length into Boyle's Law. (P_atm + 5 cmHg) × 26 cm = (P_atm - 5 cmHg) × 30 cm Step 4: Solve for P_atm. 26 P_atm + 26 × 5 = 30 P_atm - 30 × 5 26 P_atm + 130 = 30 P_atm - 150 130 + 150 = 30 P_atm - 26 P_atm 280 = 4 P_atm P_atm = (280)/(4) P_atm = 70 cmHg The value of the atmospheric pressure is 70 cmHg. c) A steel cylinder of capacity 0.5 m^3 contains nitrogen at a pressure of 30,000 Pa when the temperature is 27^ C. What will be the pressure of nitrogen if it is allowed to flow into another cylinder of capacity 9.5 m^3 with the temperature reduced to -23^ C? Step 1: Identify the initial conditions (P_1, V_1, T_1). Initial volume, V_1 = 0.5 m^3 Initial pressure, P_1 = 30,000 Pa Initial temperature, T_1 = 27^ C. Convert to Kelvin: T_1 = 27 + 273.15 = 300.15 K Step 2: Identify the final conditions (V_2, T_2) and the unknown (P_2). The gas flows into another cylinder of capacity 9.5 m^3. The total final volume is the sum of the capacities of both cylinders: Final volume, V_2 = 0.5 m^3 + 9.5 m^3 = 10 m^3 Final temperature, T_2 = -23^ C. Convert to Kelvin: T_2 = -23 + 273.15 = 250.15 K Final pressure, P_2 = ? Step 3: Apply the Combined Gas Law. The Combined Gas Law is given by: (P_1V_1)/(T_1) = (P_2V_2)/(T_2) Step 4: Substitute the values and solve for P_2. (30,000 Pa)(0.5 m^3)300.15 K = P_2(10 m^3)250.15 K P_2 = (30,000 Pa)(0.5 m^3)(250.15 K)(300.15 K)(10 m^3) P_2 = (15000 × 250.15)/(300.15 × 10) P_2 = (3752250)/(3001.5) P_2 ≈ 1250.12 Pa The pressure of nitrogen will be 1250.12 Pa. 16. a) State Archimedes principle. Archimedes' principle states that when an object is wholly or partially immersed in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the object. b) State one way of making a hydrometer more sensitive. One way to make a hydrometer more sensitive is to increase the length of its stem or decrease the diameter of its stem. Last free one today — make it count tomorrow, or type /upgrade for unlimited.