A gas is found to obey P2 V= constant. The initial temperature and volume of gas are T0 and V0. If the gas expands to volume 3 V0, then the final temperature of gas is √n T0. Find n.

Question

A gas is found to obey P2 V= constant. The initial temperature and volume of gas are T0 and V0. If the gas expands to volume 3 V0, then the final temperature of gas is √n T0. Find n. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

P2 V= Constant Also, (P V/T)= Constant ⇒ (T2/V2) V= Constant ∴ T2 V-1= Constant ∴ Tf2=T02((3 V0/V0)) ⇒ Tf=√3 T0

Q. A gas is found to obey $P^{2} V =$ constant. The initial temperature and volume of gas are $T_{0}$ and $V_{0}$ . If the gas expands to volume $3 V_{0}$ , then the final temperature of gas is $n T_{0}$ . Find $n$ .

$P^{2} V =$ Constant
Also, $\frac{P V}{T} =$ Constant
$\Rightarrow \frac{T ^{2}}{V ^{2}} V =$ Constant
$∴ T^{2} V^{- 1} =$ Constant
$∴ T_{f}^{2} = T_{0}^{2} (\frac{3 V _{0}}{V _{0}})$
$\Rightarrow T_{f} = 3 T_{0}$

Q. A gas is found to obey P2V= constant. The initial temperature and volume of gas are T0​ and V0​. If the gas expands to volume 3V0​, then the final temperature of gas is n​T0​. Find n.

P2V= Constant Also, TPV​= Constant ⇒V2T2​V= Constant ∴T2V−1= Constant ∴Tf2​=T02​(V0​3V0​​) ⇒Tf​=3​T0​

Q. A gas is found to obey $P^{2} V =$ constant. The initial temperature and volume of gas are $T_{0}$ and $V_{0}$ . If the gas expands to volume $3 V_{0}$ , then the final temperature of gas is $n T_{0}$ . Find $n$ .

$P^{2} V =$ Constant
Also, $\frac{P V}{T} =$ Constant
$\Rightarrow \frac{T ^{2}}{V ^{2}} V =$ Constant
$∴ T^{2} V^{- 1} =$ Constant
$∴ T_{f}^{2} = T_{0}^{2} (\frac{3 V _{0}}{V _{0}})$
$\Rightarrow T_{f} = 3 T_{0}$