Two containers of equal volume contain identi | vedclass

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

Question

(B) The total number of moles of the gas remains conserved when the two containers are joined.The number of moles in the first container is $n_1 = \fr

Vedclass · Accepted Answer

$P = \frac{1}{2}\left( {\frac{{{P_1}}}{{{T_1}}} + \frac{{{P_2}}}{{{T_2}}}} \right)T$

Vedclass · Answer

(B) The total number of moles of the gas remains conserved when the two containers are joined.The number of moles in the first container is $n_1 = \frac{P_1 V}{R T_1}$.The number of moles in the second container is $n_2 = \frac{P_2 V}{R T_2}$.After joining,the total volume becomes $2V$,and the gas reaches a common pressure $P$ and temperature $T$. The total number of moles is $n = n_1 + n_2 = \frac{P(2V)}{RT}$.Equating the total moles:$\frac{P_1 V}{R T_1} + \frac{P_2 V}{R T_2} = \frac{P(2V)}{RT}$Dividing both sides by $V/R$:$\frac{P_1}{T_1} + \frac{P_2}{T_2} = \frac{2P}{T}$Rearranging for $P$:$P = \frac{1}{2} \left( \frac{P_1}{T_1} + \frac{P_2}{T_2} \right) T$

Two containers of equal volume contain identical gases at pressures $P_1$ and $P_2$ and absolute temperatures $T_1$ and $T_2$ respectively. The vessels are joined and the gas reaches a common pressure $P$ and a common temperature $T$. Then:

Similar Questions

One litre of oxygen at a pressure of $1 \,atm$ and two litres of nitrogen at a pressure of $0.5 \,atm$ are introduced into a vessel of volume $1 \,L$. If there is no change in temperature, the final pressure of the mixture of gas (in $atm$) is

Three moles of oxygen are mixed with $2 \, moles$ of helium. What will be the ratio of specific heats at constant pressure and constant volume for the mixture?

Two monoatomic ideal gases at temperatures $T_1$ and $T_2$ are mixed. There is no loss of energy. If the masses of molecules of the two gases are $m_1$ and $m_2$ and the number of their molecules are $n_1$ and $n_2$ respectively,the temperature of the mixture will be:

$A$ cylindrical container of volume $4.0 \times 10^{-3} \, m^3$ contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is $400 \, K$. The pressure of the mixture of gases is:
[Take gas constant as $R = 8.3 \, J \, mol^{-1} \, K^{-1}$]

Two moles of a monoatomic gas are mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module