How many times more ignition energy is required to achieve i

How many times more ignition energy is required to achieve ignition of a fuel-air mixture at sea level with T=298 K than at altitude of 6000m where P=47,166 Pa and T=248K? Discuss the implications of your calculations for high altitude relight in aircraft gas turbine engines.

Solution

Atmospheric pressure is approx 101325 pa, Temp 298 K

apply perfect gas eqn P= rho *T*R = rho* R *298 state 1

ratio of the density of fuel is (P/T)1/(P/T)2 = 101325/298* 248/47166 =1.788 (state1/ state 2)

Assuming all other calorific values are same, the density at high altitude is .559 that at sea level

Hence proprotionately less energy   reqd to combust same volme of mixture