Two spherical vessels of equal volume V are c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the initial pressure be $P = 1 	ext{ atm}$ and initial temperature be $T = 300 	ext{ K}$.The total number of moles of gas in the system is c

Vedclass · Accepted Answer

$1.33$

Vedclass · Answer

(C) Let the initial pressure be $P = 1 	ext{ atm}$ and initial temperature be $T = 300 	ext{ K}$.The total number of moles of gas in the system is constant.Initial moles: $\mu = \frac{PV}{RT} + \frac{PV}{RT} = \frac{2PV}{RT}$.Let the final common pressure be $P'$.Final moles: $\mu' = \frac{P'V}{RT_1} + \frac{P'V}{RT_2}$,where $T_1 = 600 	ext{ K}$ and $T_2 = 300 	ext{ K}$.Since $\mu = \mu'$,we have: $\frac{2PV}{RT} = \frac{P'V}{RT_1} + \frac{P'V}{RT_2}$.Canceling $V/R$ from both sides: $\frac{2P}{T} = P' \left( \frac{1}{T_1} + \frac{1}{T_2} ight) = P' \left( \frac{T_1 + T_2}{T_1 T_2} ight)$.Solving for $P'$: $P' = \frac{2P T_1 T_2}{T(T_1 + T_2)}$.Substituting the values: $P' = \frac{2 	imes 1 	imes 600 	imes 300}{300 	imes (600 + 300)} = \frac{2 	imes 600}{900} = \frac{1200}{900} = \frac{4}{3} \approx 1.33 	ext{ atm}$.

Similar Questions

The volume of a gas at $30^{\circ} C$ temperature and $760 \ mm$ of $Hg$ pressure is $100 \ cc$. Then its volume at the same temperature and $400 \ mm$ of $Hg$ is (in $cc$)

What is the mass of $2$ litres of nitrogen gas $(N_2)$ at $22.4$ atmospheric pressure and $273\,K$?

The figure shows the $P-V$ diagram of two different masses $m_1$ and $m_2$ of the same gas drawn at a constant temperature $T$. Then:

$S.I.$ unit of universal gas constant is

Vedclass Test Series

Exam Paper Generator

Online Exam Module