For the following problem... I found the second pressure by solving P1V1/T1 = P2V2/T2. The Volumes is const so those cancel and then i am able to find the P2. From there i looked at the 1st law and came up with delt U = Qin which = mCvdelta T but that is where I am stuck. Can anyone give me a push?
3.3 A closed rigid tank with a volume of 2 m3 contains hydrogen gas initially at 320 K and 180 kpa. Heat transfer from a reservoir at 500 K takes place until the gas temperature reaches 400 K.
a) Calculate the entropy change (kJ/K) and entropy generation (kJ/K) for the hydrogen gas during the process if the boundary temperature for the gas is the same as the as the gas temperature throughout the process. (0.6264, 0 kJ/K)
b) Determine the entropy generation (kJ/K) for an enlarged system which includes the tank and the reservoir (0.1772 kJ/K)
c) Explain why the entropy generation values differ for parts a) and b)
d) Find the entropy generation for the gas and the total value (kJ/kg) if the system boundary temperature is 450 K throughout the process. (0.1273, 0.1772 kJ/K)
e) The hydrogen gas process is repeated, but paddle-wheel work is used instead of heat transfer. Calculate the entropy generation is this case. (0.6264 kJ/K)
f) Compare the relative irreversibility of processes a), d.) or e)
To solve this problem, let's break it down step by step:
Step 1: Finding the second pressure (P2)
You correctly used the ideal gas law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature. Since the volume V is constant, you correctly canceled it out. Solving for P2 using P1V1/T1 = P2V2/T2 is the right approach to find the second pressure.
Step 2: Finding the change in internal energy (ΔU)
The first law of thermodynamics states that the change in internal energy (ΔU) of a closed system is equal to the heat transferred (Q) minus the work done (W) on the system. In this case, since the process is isochoric (constant volume), there is no work done (W = 0). Therefore, ΔU = Q.
Step 3: Calculating the change in internal energy (ΔU)
To calculate the change in internal energy, you correctly used the equation ΔU = mcΔT, where m is the mass of the gas, c is the specific heat capacity of the gas at constant volume (Cv), and ΔT is the change in temperature. However, in this problem, the mass (m) is not given. Instead, we are given the volume of the tank (2 m3) and the initial conditions (temperature and pressure). To find the mass, you need to use the ideal gas law equation PV = nRT and solve for n (number of moles of gas). Then, use the molar mass of hydrogen gas to calculate the mass.
Step 4: Calculating the entropy change (ΔS)
The entropy change (ΔS) can be calculated using the equation ΔS = ∫(Qrev/T), where ∫ represents the integral and Qrev is the heat transferred reversibly. In this problem, we are assuming that the boundary temperature for the gas is the same as the gas temperature throughout the process. Therefore, the heat transferred (Q) can be obtained from the change in internal energy (ΔU) calculated in Step 3, and the temperature (T) remains constant throughout the process.
Step 5: Calculating the entropy generation (ΔSgen)
The entropy generation (ΔSgen) can be calculated using the equation ΔSgen = ΔS - Qrev/T. In this problem, we are given the entropy change (ΔS) and the heat transferred reversibly (Qrev) from Step 4. So, just substitute those values into the equation to find the entropy generation.
Step 6: Comparing the values of entropy generation
For parts a) and b), the entropy generation values differ because part b) considers an enlarged system that includes both the tank and the reservoir. This allows for additional entropy generation due to heat transfer between the tank and the reservoir.
For part d), where the system boundary temperature is 450 K throughout the process, you can follow the same steps (1-5) to calculate the entropy generation.
For part e), where paddle-wheel work is used instead of heat transfer, you will need to use a different equation to calculate the entropy generation. The equation for entropy generation in this case depends on the specific situation and details of the paddle-wheel work process and is not provided in the problem statement.
Finally, to compare the relative irreversibility of processes a), d), and e), you need to compare the values of entropy generation obtained in each case. The process with a higher entropy generation is considered more irreversible.