
Joule-Thomson coefficient is zero at:
A. critical temperature
B. inversion temperature
C. Absolute temperature
D. Baoyle’s temperature
Answer
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Hint: we will substitute the value of critical temperature, inversion temperature and Boule temperature in Joule- Thomson coefficient formula and determine the temperature at which it becomes zero. The critical temperature is the temperature, below which a gas can be liquefied. Inversion temperature is the temperature, at which the value of van der waals constant a, and b becomes equal.
Complete step by step solution:
In the joule-Thomson experiment, a gas expands from initial high pressure to final low pressure under adiabatic condition.
The value of joule-Thomson coefficient is as follows:
is known as Joule-Thomson coefficient .
For the van der waals gas the value of Joule-Thomson coefficient is as follows:
The formula of critical temperature is as follows:
So, when
The formula of inversion temperature is as follows:
Inversion temperature is the temperature, below which if the gas is allowed to expand it shows the cooling effect and above the inversion temperature gas shows the heating effect so, it is not the highest temperature at which vapour pressure of a liquid can be measured.
So, when
The formula of Boyle’s temperature is as follows:
So, when
So, Joule-Thomson coefficient is zero at inversion temperature.
Therefore, option (B) inversion temperature is correct.
Note: Joule-Thomson process is an isenthalpic process. For ideal gas according to the ideal gas equation, the value of is,
On substituting the value of in ,
So, for ideal gas, the Joule-Thomson coefficient is always zero. For real gas it becomes zero at inversion temperature.
Complete step by step solution:
In the joule-Thomson experiment, a gas expands from initial high pressure to final low pressure under adiabatic condition.
The value of joule-Thomson coefficient is as follows:
For the van der waals gas the value of Joule-Thomson coefficient is as follows:
The formula of critical temperature is as follows:
So, when
The formula of inversion temperature is as follows:
Inversion temperature is the temperature, below which if the gas is allowed to expand it shows the cooling effect and above the inversion temperature gas shows the heating effect so, it is not the highest temperature at which vapour pressure of a liquid can be measured.
So, when
The formula of Boyle’s temperature is as follows:
So, when
So, Joule-Thomson coefficient is zero at inversion temperature.
Therefore, option (B) inversion temperature is correct.
Note: Joule-Thomson process is an isenthalpic process. For ideal gas according to the ideal gas equation, the value of
On substituting the value of
So, for ideal gas, the Joule-Thomson coefficient is always zero. For real gas it becomes zero at inversion temperature.
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