Methane and oxygen exist in a stoichiometric mixture at 500 kPa and 298 K. They
ID: 1767374 • Letter: M
Question
Methane and oxygen exist in a stoichiometric mixture at 500 kPa and 298 K. They are ignited and react at constant volume. Combustion is complete. a. Find the heat removed from the system per kmol of fuel if the final products are at 1500 K. b. What is the final pressure? c. Explain what assumptions made in this calculation are less accurate for constant volume 1. combustion than for the constant pressure combustion we have studied before. 2. If the reaction above occurs in an insulated container, find the final temperature and pressure of the products.Explanation / Answer
Complete combustion of methane and oxygen is (CH4 +2O2=CO2+2H2O)
TOTAL HEAT REJECTED FROM THE SYSTEM AT CONSTANT VOLUME IS m*C*TEMP. DIFFERENCE
SO TOATAL 3 MOL AVAILAVLE IN THE SYSTEM SO MASSS OF THE SYSTEM IS 80/3 KG/KMOL
SPECIFIC HEAT AT CONSTANT VOLUME IS .718KJ/KG-K
TOTAL HEAT REJECTED FROM SYSTEM IS =80/3*.718*(1500-298)=23014.29KJ/KMOL
b. USING IDEAL GAS EQUATION P1V1/T1=P2V2/T2 IMPLIES THAT P1/T1=P2/T2
P2=500*298/1500=99.33KPA
C. IF WE INCREASE THE TEMPERATURE OF THE SYSTEM AT CONSTANT VOLUME IT WILL JUST INCREASE THE INTERNAL ENERGY OF THE SYSTEM .SO TOTAL HEAT TRANSFER FROM THE SYSTEM IS LESS ACCORDING TO THE FIRST LAW OF THERMODYNAMICS. dq=du+pdv. BUT IF WE INCREASE THE TEMPERATURE AT CONSTANT PRESSURE IT WILL INCREASE INTERNAL ENERGY AS WELL AS DO SOME EXTERNAL WORK.THATS WHY TOTAL HEAT TRANSFER FROM SYSTEM IS HIGH AT CONSTANT PRESSURE
2.