Question

If the critical temperature of a gas is $100K$ then its Boyle temperature will be-
A.$333K$
B.$103K$
C.$337K$
D.$500K$

Answer 1

We need to know that the critical temperature is equal to the temperature of a gas when it is in critical state and at the pressure is alone, the gas cannot be liquefied and it does not depend on the pressure which is applied. Therefore, the critical temperature is equal to the highest temperature at which the substance lives in a liquid state. And the critical pressure is equal to the vapour pressure when it is in critical pressure.

Complete answer:
The Boyle temperature of the gas is not equal to $33.3K$. Hence, option (A) is incorrect.
The Boyle temperature of the gas is not equal to $103K$. Hence, option (B) is incorrect.
The Boyle temperature of the gas is equal to $337K$.
According to the question, the critical temperature is equal to $100K$.
The equation which is used to find out the critical temperature is,
${T_c} = \dfrac{8}{{27}}{T_B}$
Where, ${T_c}$ is equal to critical temperature and ${T_B}$ is equal to Boyle temperature. By rearranging and substitute the value of critical temperature in the above equation will get;
${T_B} = \dfrac{{100 \times 27}}{8} = 337K$
Hence, option (C) is correct.
The Boyle temperature of the gas is not equal to $500K$. Hence, option (D) is incorrect.

Hence, option (C) is correct.

Note:
The Boyle temperature of a gas can be found by using critical temperature. The Boyle temperature is equal to the temperature at which the second virial coefficient equals zero. And at Boyle temperature, the repulsive forces and attractive forces will balance by acting on the gas particles. And at a pressure range, the real gas will start to act like an ideal gas.