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

When the volume of a system is increased two times and the temperature is decreased to half of its initial temperature,then the pressure becomes ...... times.

The mass of oxygen gas occupying a volume of $11.2 \text{ litres}$ at a temperature $27^{\circ}C$ and a pressure of $760 \text{ mm}$ of mercury in kilograms is $[$ Molecular weight of oxygen $= 32]$

$A$ fixed amount of gas has a volume $V$ at constant pressure. If the temperature of the gas is increased such that the $v_{rms}$ of the molecules doubles,then its new volume will be .......

An insulated cylinder of volume $60\,cm^{3}$ is filled with a gas at $27^{\circ}C$ and $2$ atmospheric pressure. Then the gas is compressed making the final volume $20\,cm^{3}$ while allowing the temperature to rise to $77^{\circ}C$. The final pressure is . . . . . . atmospheric pressure.

For an ideal gas,the density of the gas is $\varrho_0$ when temperature and pressure of the gas are $T_0$ and $P_0$ respectively. When the temperature of the gas is $2 T_0$,its pressure becomes $3 P_0$. The new density will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module