A specific volume of dry air is expanded to 6 times it volume at standard pressure and temperature under Adiabatic condition and isothermal condition in each cases evaluate the final temperature and pressure.Given that the specific gas ratio gamma=1.40 for air.
How I don't understand the question
The question asks you to evaluate the final temperature and pressure of a specific volume of dry air when it is expanded under adiabatic and isothermal conditions, respectively.
In both cases, the initial volume of the air is expanded to 6 times its original volume. Since the expansion is adiabatic, it means there is no heat exchange with the surrounding during the process. On the other hand, isothermal condition means that the temperature of the air remains unchanged throughout the expansion.
To solve these problems, we can use the adiabatic and isothermal equations:
For adiabatic expansion: Pv^gamma = constant
For isothermal expansion: PV = constant
Now let's calculate the final temperature and pressure for each condition:
1. Adiabatic condition:
Using the adiabatic equation, we have:
(P1)(V1^gamma) = (P2)(V2^gamma)
Since the volume is expanded to 6 times, we can write:
(P1)(V1^gamma) = (P2)(6V1^gamma)
The constant factor cancels out, and we are left with:
P1 = 6P2
Now we can calculate the final pressure using this equation.
2. Isothermal condition:
Using the isothermal equation, we have:
(P1)(V1) = (P2)(V2)
Again, since the volume is expanded to 6 times, we can write:
(P1)(V1) = (P2)(6V1)
Dividing both sides by 6V1, we get:
(P1)/6 = P2
Now we can calculate the final pressure using this equation.
To calculate the final temperature, since the process is isothermal, it remains unchanged and equal to the initial temperature.
So, to summarize:
- In adiabatic condition: final pressure is 6 times the initial pressure, final temperature is equal to the initial temperature.
- In isothermal condition: final pressure is 1/6 times the initial pressure, final temperature is equal to the initial temperature.
Note: Always make sure to double-check the equations and calculations, and consider the units used in the problem.