What mass of natural gas (CH4) would be required to cook a 19 lb (8.62 kg) turkey at room temperature (20.5°C) to an internal temperature of 165°F (73.9°C) in a 71.4 % efficient natural gas oven? The specific heat capacity of the turkey is 6.018 J/g°C.
You have three problems here.
1. You need to calculate the amount of heat required to cook the turkey.
2. You need to calculate the amount of heat given off by the methane gas in cooking.
3. You don't have the heat of combustion from the methane.
#1. q = neat needed to cook turkey = mass turkey x specific heat turkey x (Tfinal - Tinitial).
q = 8620 g x 6.018 J/g*C x (73.9 - 20.5) = approximately 770,000 J
#2. CH4 + 2O2 ==> CO2 + 2H2O
I looked up the heat of combustion of CH4 on the web and found 889 kJ/mol. That is 889 kJ/16 grams.
CH4 needed is 16 g CH4 x (770 kJ/889 kJ) = approx 14 g CH4 of at 100%.
14/0.714 = 19 g CH4.
Note these are estimates. You should confirm each calculation to the number of significant figures you want.