one more question:

a worker cleans a railroad car with steam of 15000ft^3 car on inside, t=240F P=14.7psia of steam. the car is closed. the steam inside cools until P=12 psia, at which time salad oil is added to tank. find a. heat transfer from steam during cooling, b. amount of liquid water in bottom of tank car that will dilute the salad oil.

I found the T2 using ideal gas law, using dU=dQ=dW, dw=0 cause no volume change. so would I just look up the values of internal energy change in a table, then what about part b?

To find the heat transfer from steam during cooling and the amount of liquid water in the bottom of the tank car, we can follow these steps:

a. Heat transfer from steam during cooling:
1. Since the process is isochoric (no volume change), as you correctly stated, the work done by the system (dw) is zero.
2. Therefore, applying the First Law of Thermodynamics (dU = dQ + dW), we can simplify it to dU = dQ.
3. Now, we need to find the change in internal energy (dU) of the steam. This can be obtained using the Ideal Gas Law: PV = nRT. We can assume that the steam behaves ideally.
4. Rearrange the Ideal Gas Law equation to solve for temperature (T2) at the final pressure (P2):
T2 = (P2 / P1) * T1 (where T1 = 240°F, P1 = 14.7 psia, and P2 = 12 psia)
5. Convert T2 from Fahrenheit to Rankine (R) by adding 459.67: T2_R = T2 + 459.67.
6. Using the internal energy change values for steam at constant volume from a table or steam tables, calculate the change in internal energy (dU) as dU = U2 - U1 (where U1 and U2 are the internal energy values at T1 and T2 respectively).
7. The value of dQ will be equal to dU.

b. Amount of liquid water in the bottom of the tank car:
1. To find the amount of liquid water, we need to determine the mass of water that condenses from the steam.
2. First, calculate the specific volume of the steam at the initial state (v1) using the ideal gas law: v1 = V1 / n (where V1 = 15000 ft^3 and n is the number of moles).
3. Using the ideal gas law, calculate the number of moles (n) of steam at the initial state: n = PV / (RT1) (where P = 14.7 psia, V is given, R is the ideal gas constant, and T1 is the initial temperature in Rankine).
4. Using the density of steam, calculate the mass of steam (m1) at the initial state: m1 = n * M (where M is the molar mass of steam).
5. The mass of water (m_water) is equal to the difference between the mass of the steam and the mass of the steam-oil mixture: m_water = m1 - m_steam_oil (where m_steam_oil is the mass of the steam-oil mixture).
6. To find the mass of salad oil and steam-oil mixture (m_steam_oil), we need to consider the molar mass of the oil and the mole fraction of the oil in the mixture. The mole fraction can be calculated using the pressure of the steam after adding the oil (P2) and the vapor pressure of the oil.
7. Finally, calculate the volume of liquid water using the density of water and the mass of water: V_water = m_water / ρ_water (where ρ_water is the density of water).

Please note that the calculations provided are simplified explanations of the steps involved in finding the answers. The actual calculations may involve units conversions and more complex equations. It is recommended to refer to appropriate thermodynamic tables or use specialized software to obtain accurate results.