On a cool (4.0o C) Saturday morning, a pilot fills the fuel tanks of her Pitts S-2C (a two-seat aerobatic airplane) to their full capacity of 106.0 L. Before flying on Sunday morning, when the temperature is again 4.0o C, she checks the fuel level and finds only 103.4 L of gasoline in the aluminum tanks. She realizes that it was hot on Saturday afternoon and that thermal expansion of the gasoline caused the missing fuel to empty out of the tank’s vent. (a) What was the maximum temperature (in oC) of the fuel and the tank on Saturday afternoon? The coefficient of volume expansion of gasoline is 9.5 X 10-4 K-1. (b) To have the maxi-mum amount of fuel available for flight, when should the pilot have filled the fuel tanks?
Solution 84P Step 1: In this question, we need to find the maximum temperature on saturday afternoon And when should pilot fill the tank to have maximum fuel Consider the data given Maximum capacity of fuel tank v = 106.0 L 0 Gain in temperature T = 4 C 0 1 Fuel available in the tank v = 203.4 L Coefficient thermal expansion of gasoline = 9.5 × 10 K 4 1 gas 6 Coefficient of thermal expansion of aluminium al = 23 × 10 K Step 2 : Let find the change in volume It if given as V = v v = 106.0 L 103.4 L = 2.6 L 0 1 We need to find change in temperature This is obtained using (Ti+4)V T initial gasalv 0 Substituting the values T = (Ti+4) 2.6 L initial 9.5×104K 23×10 6K ×106.0 L Resolving this we get T = 26 C 0 i 0 0 0 Hence the maximum temperature gained us 126 C + 4 C = 30 C