Question

An ideal gas can be expanded from an initial state to a certain volume through two different processes (i) $P{V}^2=constantand\left(ii\right)P=K{V}^2$ where K is a positive constant. Based on the given situation, choose the correct statements

• A. Final temperature in (ii) will be greater than in (i)
• B. Final temperature in (ii) will be less than in (i)
• C. Total heat given to the gas in case (ii) is greater than in (i)
• D. Total heat given to the gas in case (ii) is less than in (i)

Answer 1

Answer: (A), (C)

The correct options are
A Final temperature in (ii) will be greater than in (i)
C Total heat given to the gas in case (ii) is greater than in (i)

Since, the question says that this is an ideal gas,
the molecules will always follow the ideal gas equation irrespective of the law that is used for the transformation.
Hence, we use P = $\frac{nRT}{V}$
This gives us a relation between T and V that can show us the variation of T as the gas is expanded.
TV = C {for the first case}
T = C $V^3$ {for the second case}
Now, in both the cases,
V is increasing as expansion is occuring.
In first case T will decrease, whereas in the second case T will increase.