Thermodynamics Question 1
Question 1 - 2024 (01 Feb Shift 1)
The pressure and volume of an ideal gas are related as $PV^{3 / 2}=K$ (Constant). The work done by gas when the gas is taken from state $A\left(P _1, V _1, T _1\right)$ to state $B\left(P _2, V _2, T _2\right)$ is :
[We modified question statement, In official NTA paper question was incomplete]
(1) $2\left(P _1 V _1-P _2 V _2\right)$
(2) $2\left(P _2 V _2-P _1 V _1\right)$
(3) $2\left(\sqrt{P _1} V _1-\sqrt{P _2} V _2\right)$
(4) $2\left(P _2 \sqrt{V _2}-P _1 \sqrt{V _1}\right)$
Show Answer
Answer: (1)
Solution:
For $PV^{x}=$ constant
If work done by gas is asked then
$W=\frac{nR \Delta T}{1-x}$
Here $x=\frac{3}{2}$
$\therefore W=\frac{P _2 V _2-P _1 V _1}{-\frac{1}{2}}$
$=2\left(P _1 V _1-P _2 V _2\right)$
Option (1) is correct
If work done by external is asked then $W=-2\left(P _1 V _1-P _2 V _2\right) \ldots \ldots$ Option (2) is correct
