Answer : The final temperature of gas is 266.12 K
Explanation :
According to the Joule-Thomson experiment, it states that when a gas is expanded adiabatically from higher pressure region to lower pressure region, the change in temperature with respect to change in pressure at constant enthalpy is known as Joule-Thomson coefficient.
The formula will be:
[tex]\mu_{J,T}=(\frac{dT}{dP})_H[/tex]
or,
[tex]\mu_{J,T}=(\frac{dT}{dP})_H\approx \frac{\Delta T}{\Delta P}[/tex]
As per question the formula will be:
[tex]\mu_{J,T}=\frac{T_2-T_1}{P_2-P_1}[/tex] .........(1)
where,
[tex]\mu_{J,T}[/tex] = Joule-Thomson coefficient of the gas = [tex]0.13K/atm[/tex]
[tex]T_1[/tex] = initial temperature = [tex]19.0^oC=273+19.0=292.0K[/tex]
[tex]T_2[/tex] = final temperature = ?
[tex]P_1[/tex] = initial pressure = 200.0 atm
[tex]P_2[/tex] = final pressure = 0.95 atm
Now put all the given values in the above equation 1, we get:
[tex]0.13K/atm=\frac{T_2-292.0K}{(0.95-200.0)atm}[/tex]
[tex]T_2=266.12K[/tex]
Therefore, the final temperature of gas is 266.12 K
