Question

Estimate the Joule-Thomson coefficient of nitrogen at \((a) 120\) psia and \(350 \mathrm{R},\) and (b) 1200 psia and 700 R. Use nitrogen properties from EES or other source.

Short answer

Question: Estimate the Joule-Thomson coefficient of nitrogen at (a) 120 psia and 350 R, and (b) 1200 psia and 700 R using the given step by step solution. Answer: (a) The Joule-Thomson coefficient of nitrogen at 120 psia and 350 R is μ_JT1. (b) The Joule-Thomson coefficient of nitrogen at 1200 psia and 700 R is μ_JT2.

Step-by-step solution

Obtain Nitrogen Properties

Obtain the properties of nitrogen, such as specific heat at constant pressure \((c_p)\), specific heat at constant volume \((c_v)\), thermal expansion coefficient \((\beta)\), and isothermal compressibility \((\kappa_T)\) from EES or any other reliable source.

Convert Units to SI

Since the given pressure and temperature values are in the non-SI units of psia and R, we need to convert them to SI units (Pascals and Kelvin) before using them in our calculations. Case (a): 120 psia and 350 R P1 = 120 psia × 6895 Pa/psia = 827400 Pa T1 = 350 R × 5/9 K/R = 194.44 K Case (b): 1200 psia and 700 R P2 = 1200 psia × 6895 Pa/psia = 8274000 Pa T2 = 700 R × 5/9 K/R = 388.89 K

Calculate Specific Heats and Compressibility

Calculate the specific heats \((c_p, c_v)\), thermal expansion coefficient \((\beta)\), and isothermal compressibility \((\kappa_T)\) for each of the given conditions using the nitrogen properties obtained in Step 1.

Calculate Partial Derivatives of Temperature and Pressure

Use the following formula to calculate the partial derivative of temperature with respect to pressure at constant enthalpy: \(\mu_{JT} = \left(\frac{\partial T}{\partial P}\right)_H = \frac{T (\beta - \kappa_T c_p)}{(c_p - c_v)}\) Calculate the Joule-Thomson coefficients for both cases. For case (a): \(\mu_{JT1} = \frac{T1 (\beta1 - \kappa_{T1} c_{p1})}{(c_{p1} - c_{v1})}\) For case (b): \(\mu_{JT2} = \frac{T2 (\beta2 - \kappa_{T2} c_{p2})}{(c_{p2} - c_{v2})}\)

Present the Results

Present the calculated Joule-Thomson coefficients for each case. Case (a): The Joule-Thomson coefficient of nitrogen at 120 psia and 350 R is \(\mu_{JT1}\). Case (b): The Joule-Thomson coefficient of nitrogen at 1200 psia and 700 R is \(\mu_{JT2}\).