Which of the following statements is correct as shown in the graph?

Options

A. The slope of Z vs. p at constant temperåture for all real gases, is `b"/"RT`.
B. The slope of Z vs. p at constant temperature for both He and `H_(2)" is "b"/"RT`.
C. The slope of Z vs. p at low pressure for all real gases, at constant temperature is `b"/"RT`.
D. The slope of Z vs. p at high pressure and at constant temperature for real gases is `-b"/"RT`.

Answer

B

Explanation

van der Waals equation is given by `(p+(n^(2)a)/(V^2))(V-b)= RT`
For `H_(2)" and "He`, force of attraction is zero. Therefore, a=0. Substituting the value of a, van der Waals equation becomes `p(V-b)= RT implies pV= RT+pb`
Dividing the above equation by RT on both the sides, we get `implies (pV)/(RT)= 1+(pb)/(RT)`
`implies Z= 1+(pb)/(RT) implies Z= ((b)/(RT))p+1`
Comparing with equation of the straight line, we get slope `=(b)/(RT)`.