Thermodynamics; Temperature in cylinder after combustion

[ChristopherJ]

Homework Statement

I have an assignment to calculate the temperature, T1, after combustion in a cylinder. The combustion itself happens at constant pressure. I also know the average molar mass, M, of the gases after combustion and that the specific heat capacity is constant and can be calculated with use of the molar mass and that the specific heat ratio K.

M = 28.71 kg/kmol
K = 1.40
Q1 = 1890 J (the heat that comes from the fuel due to combustion
V0 = 0.002 m^3 (the volume of the cylinder)
p0 = 1.013*10^-5 Pa (pressure in cylinder before compression
T0 = 293.15 K (temperature of the air before compression)
m_fuel = 45.0*10^3 kg (fuel in cylinder)
m_air = 2.40*10^-3 kg (air in cylinder)

Homework Equations

My assumption is, considering that it is stated in the task that the combustion happens at constant pressure, that this is an isobaric process.

This yields that p0 = p1 and that V1/V0 = T1/T0.

q_r = c_p*(T1-T0).

c_p = K*8314.3/(M*(K-1))

Here I don't know q_r (what is that?) and V1.

Another equation from which I can get T1 is: Q1 = n*c_p*T_delta, where n is that number of moles.

The Attempt at a Solution

Using the equations above: c_p = 1013.53 => T_delta = Q1/(n*c_p) = 1890/(n*c_p).

Here I'm not sure about n. Is it the moles of fuel (C4H10) or fuel and air?

Using moles of fuel: T_delta = 1890/(7.76*10^-4*1013.53) = 777.29 K.

I'm really lost here. Is then T1 = T_delta-T0 = 777.29-293.15 (= 484.14 degree Celsius)?

Is my assumption of isobaric process correct? And can I really use the temperature T0 since that is before compression?

I would really appreciate some help with this!

Best regards
Christopher

 

[anathema]

Hello Christopher,

It seems like you are on the right track with your calculations. Here are some tips that may help you solve this problem:

1. Isobaric process: Your assumption of an isobaric process is correct since the problem states that combustion occurs at constant pressure. This means that the pressure remains constant throughout the process, so p0 = p1.

2. Specific heat ratio: The specific heat ratio (K) is given in the problem and it is used to calculate the specific heat capacity (c_p) of the gases after combustion. This is because the specific heat capacity is not constant and varies with temperature and pressure. So, use the equation c_p = K*8314.3/(M*(K-1)) to calculate the specific heat capacity.

3. q_r: q_r is the heat released during combustion, which is given in the problem as Q1. This value is used in the equation q_r = c_p*(T1-T0) to calculate the change in temperature.

4. Number of moles: The number of moles (n) that you need to use in the equation Q1 = n*c_p*T_delta is the total number of moles of both fuel and air. This is because both fuel (C4H10) and air (N2 and O2) are involved in the combustion process.

5. Volume: You are correct in assuming that V1/V0 = T1/T0. So, you can use this relationship to calculate the final volume (V1) of the gases after combustion.

6. Temperature calculation: Once you have calculated the specific heat capacity (c_p), q_r, and V1, you can use the equations above to solve for T1. Your final answer should be in Kelvin, not Celsius.

I hope this helps! Let me know if you have any further questions. Good luck with your assignment!