During an experiment, an ideal gas is found to obey an additional law VP2 = constant. The gas is initially at temperature T and volume V. When it expands to a volume 2 V, the temperature becomes

Question

During an experiment, an ideal gas is found to obey an additional law VP2 = constant. The gas is initially at temperature T and volume V. When it expands to a volume 2 V, the temperature becomes (A) T (B) 2 T (C) T√2 (D) T/2

Tardigrade Admin · Accepted Answer

V P2= constant or P V1 / 2=K (P V/T)= constant ⇒ (V/T)((K/V(1)2))= constant ⇒ (V(1/2)/T)= constant or ((2 V)(1/2)/T')=(V(1/2)/T) or T'=T √2.

Q. During an experiment, an ideal gas is found to obey an additional law $V P^{2} =$ constant. The gas is initially at temperature $T$ and volume $V$ . When it expands to a volume 2 V, the temperature becomes

T

2 T

$T 2$

T/2

$V P^{2} =$ constant or $P V^{1/2} = K$
$\frac{P V}{T} =$ constant
$\Rightarrow \frac{V}{T} (\frac{K}{V ^{\frac{1}{2}}}) =$ constant
$\Rightarrow \frac{V ^{\frac{1}{2}}}{T} =$ constant
or $\frac{( 2 V ) ^{\frac{1}{2}}}{T ^{'}} = \frac{V ^{\frac{1}{2}}}{T}$ or
$T^{'} = T 2$ .

Q. During an experiment, an ideal gas is found to obey an additional law VP2= constant. The gas is initially at temperature T and volume V. When it expands to a volume 2 V, the temperature becomes

T

2 T

T2​

T/2

VP2= constant or PV1/2=K TPV​= constant ⇒TV​(V21​K​)= constant ⇒TV21​​= constant or T′(2V)21​​=TV21​​ or T′=T2​.

Q. During an experiment, an ideal gas is found to obey an additional law $V P^{2} =$ constant. The gas is initially at temperature $T$ and volume $V$ . When it expands to a volume 2 V, the temperature becomes

$T 2$

$V P^{2} =$ constant or $P V^{1/2} = K$
$\frac{P V}{T} =$ constant
$\Rightarrow \frac{V}{T} (\frac{K}{V ^{\frac{1}{2}}}) =$ constant
$\Rightarrow \frac{V ^{\frac{1}{2}}}{T} =$ constant
or $\frac{( 2 V ) ^{\frac{1}{2}}}{T ^{'}} = \frac{V ^{\frac{1}{2}}}{T}$ or
$T^{'} = T 2$ .