Here is the question, explain why 9/10 was used to multiply 500: Find out the speed at which a four-cylinder engine using natural gas can develop a brake power of 50kW working under following conditions. Air-gas ratio 9:1, calorific value of the fuel = 34 MJ/m³, compression ratio 10:1, volumetric efficiency = 70%, indicated thermal efficiency = 35% and the mechanical efficiency = 80% and the total volume of the engine is 2 litres.

The value of 500 cc represents the total volume (V_tot) of one cylinder when the piston is at its lowest point (Bottom Dead Center, BDC). This total volume is the sum of the swept volume (V_s) and the clearance volume (V_c). The compression ratio (CR) is given as 10:1. The compression ratio is defined as: CR = Total VolumeClearance Volume = (V_s + V_c)/(V_c) From this definition, we can also express the swept volume (V_s) in terms of the total volume (V_tot) and the compression ratio (CR). We know that V_tot = V_s + V_c. From the compression ratio definition: CR = V_totV_c V_c = V_totCR Now substitute V_c back into the equation for V_tot: V_tot = V_s + V_totCR Rearrange to solve for V_s: V_s = V_tot - V_totCR V_s = V_tot (1 - (1)/(CR)) V_s = V_tot ((CR - 1)/(CR)) Given: V_tot per cylinder = 500 cc (from the previous step, 2 litres / 4 cylinders = 0.5 litres = 500 cc) CR = 10 Substitute these values into the formula for V_s: V_s = 500 cc × ((10 - 1)/(10)) V_s = 500 cc × ((9)/(10)) Therefore, (9)/(10) is used to multiply 500 cc to calculate the swept volume (V_s) per cylinder, which is the volume displaced by the piston as it moves from Bottom Dead Center (BDC) to Top Dead Center (TDC).