Air is added in to a flat tire

[blue89]

[bpump add air into the flat tire in the gas station. The compressed air is at 180 psia and 60F(+460). the tire is initially at vaccum, therefore p0=0 psia. Air is added into the tire until it reaches Pf =32.9 psig which is (23.9+14.7=47.6 psia), then stopped . this process is adiobatic which mean Q=0. find the final tempreture Tf in R degree. then find the entropy change and internal changed for a rigid tire which has volume of 0.6 cuft. what is the system (control mass or control volume . In this cas Air is an ideal gas with cp=7/2 R

 

[Valkarie]

and R=17.3 in2/RlbmSystem: Control Volume The final temperature of the air in the tire can be calculated by using the ideal gas law, with the initial pressure of 0 psia and the final pressure of 47.6 psia. PfV/Tf = PiV/Ti47.6 psia * 0.6 cuft / Tf = 0 psia * 0.6 cuft / 460RTf = 806.3 RThe entropy change of the system is calculated by using the equation ΔS = cv ln(Tf/Ti) + R ln(Vf/Vi)Where cv is the constant volume specific heat capacity, R is the gas constant, and Vf/Vi is the change in volume of the system. ΔS = (7/2 * 17.3) ln(806.3/460) + 17.3 ln(1/1) ΔS = 32.2 in2/RlbmThe internal energy change of the system is calculated by using the equation ΔU = cv (Tf - Ti)Where cv is the constant volume specific heat capacity.ΔU = (7/2 * 17.3) (806.3 - 460) ΔU = 602.4 in2/Rlbm

 

[piercas]

]

I would like to clarify a few points in this scenario. First, it is important to note that the air being added to the tire is not at 180 psia, but rather at 180 psig (gauge pressure). This means that the absolute pressure of the air is actually 194.7 psia (180 psig + 14.7 psia atmospheric pressure). This distinction is important because it affects the calculations for temperature and internal energy.

Next, the assumption that the tire is initially at vacuum is not realistic. In reality, there will always be some atmospheric pressure inside the tire, even if it is very low. Therefore, the initial pressure should be taken as slightly above 0 psia, rather than exactly 0 psia.

Using the ideal gas law (P1V1/T1 = P2V2/T2), we can calculate the initial temperature of the air inside the tire to be approximately 60.9 degrees Fahrenheit (T1 = (P2V2/T2) * (P1V1)). This is assuming that the volume of the tire remains constant at 0.6 cuft throughout the process.

To find the final temperature (Tf), we can use the adiabatic process equation (P1V1^γ = P2V2^γ) where γ is the ratio of specific heats, which for an ideal gas with cp=7/2 R is equal to 1.4. Solving for Tf, we get Tf = 71.4 degrees Fahrenheit.

To calculate the entropy change (ΔS), we can use the equation ΔS = cp*ln(Tf/T1) - R*ln(Pf/P1). Plugging in the values, we get ΔS = 0.449 R. This means that the entropy of the system has increased during this process.

As for the internal energy change (ΔU), we can use the equation ΔU = cp*(Tf-T1) - R*(ln(Tf/T1)+ln(Pf/P1)). Plugging in the values, we get ΔU = 2.085 R. This means that the internal energy of the system has also increased.

Finally, to answer the question of whether the system is a control mass or control volume, we can consider the fact that the volume of the tire remains constant throughout the process. This means that the tire is a rigid container