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Chapter 1: Problem 53

Develop a computer progrem for calculating the density of an ideal gas when the gas pressure in pascals (abs), the temperature in degrees Celsius, and the gas constant in \(\mathrm{J} / \mathrm{kg} \cdot \mathrm{K}\) are specified. Plot the density of helium as a function of temperature from \(0^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\) and pressures of \(50,100,150,\) and \(200 \mathrm{kPa}(\mathrm{abs})\).

Short Answer

Expert verified
The program will calculate the density of helium (an ideal gas) using the adapted ideal gas law, and then plot these calculated densities along with a specified temperature range (0-200°C) at four different given pressures (50, 100, 150, 200 kPa). A total of four plots will be presented in the end.

Step by step solution

01

Conversion of Temperature to Kelvin

The given temperature is in Celsius and needs to be converted into Kelvin as gas constant R_s is in J/kg·K. The conversion formula \( K = °C + 273.15 \) will be used.
02

Apply the ideal gas law equation

Use the modified formula of ideal gas law to calculate the density, \( \rho = \frac{P} {R_{s}*T} \). It's important to ensure the units are consistent: P is pressure in pascals, R_s is specific gas constant given by the problem in J/kg·K, and T is temperature in Kelvin.
03

Plotting the density of helium

Use the calculated density values of helium to draw a graph where the X-axis represents the temperature range (0 to 200°C) and the Y-axis represents the density of helium. Repeat this process for the four specified pressures (50,100,150, and 200 kPa). As a result, four different plots will be generated on the graph.

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