Question

Assertion
The value of Boyle’s temperature for a real gas is $\left( {{{\text{T}}_{\text{B}}}\,{\text{ = }}\,\dfrac{{\text{a}}}{{{\text{Rb}}}}} \right)$
Reason
At Boyle’s temperature, ${{\text{T}}_{\text{B}}}$, real gases behave ideally over a long range of pressure.
(A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
(B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
(C) Assertion is correct but Reason is incorrect.
(D) Assertion is incorrect but Reason is correct.

Answer 1

Hint: The temperature at which the second virial coefficient, ${{\text{B}}_{\text{2}}}\left( {\text{T}} \right)$, becomes zero is known as the Boyle temperature. At this temperature, the attractive and repulsive forces acting on the gas particles balance each other out.

Complete answer:
Boyle temperature, also known as Boyle poin, is the temperature at which a natural gas acts as an ideal gas over a large range of pressures ($100$ atm).
 $\left( {{{\text{T}}_{\text{B}}}\,{\text{ = }}\,\dfrac{{\text{a}}}{{{\text{Rb}}}}} \right)$ is the Boyle Temperature for real gas.
As the temperature exceeds the Boyle temperature, the gas tends to act as an ideal gas over a wider range of pressures since higher order virial coefficients are usually much smaller than the second coefficient.
Hence, both Assertion and Reason are correct and Reason is the correct explanation for Assertion. So, the correct option is (A).

Note:
When pressures are low, the second virial coefficient would be the only one that matters since the others are concerned with terms of higher order on the pressure. Similarly, at Boyle temperature, the dip in a PV diagram tends to become a straight line over time.