Two ideal polyatomic gases at temperatures T_ | vedclass

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

Question

(B) Let the final temperature of the mixture be $T$. Since there is no loss of energy,the total internal energy of the system is conserved.The interna

Vedclass · Accepted Answer

$\frac{n_{1}F_{1}T_{1} + n_{2}F_{2}T_{2}}{n_{1}F_{1} + n_{2}F_{2}}$

Vedclass · Answer

(B) Let the final temperature of the mixture be $T$. Since there is no loss of energy,the total internal energy of the system is conserved.The internal energy of a gas is given by $U = \frac{F}{2} n R T$,where $n$ is the number of moles. Since $n$ is proportional to the number of molecules $N$,we can write $U = \frac{F}{2} N k_{B} T$.For the mixture,the total energy before mixing equals the total energy after mixing:$U_{1} + U_{2} = U_{mix}$$\frac{F_{1}}{2} n_{1} k_{B} T_{1} + \frac{F_{2}}{2} n_{2} k_{B} T_{2} = \frac{F_{1}}{2} n_{1} k_{B} T + \frac{F_{2}}{2} n_{2} k_{B} T$Canceling the common terms $\frac{1}{2} k_{B}$ from both sides:$F_{1} n_{1} T_{1} + F_{2} n_{2} T_{2} = T (F_{1} n_{1} + F_{2} n_{2})$Solving for $T$:$T = \frac{F_{1} n_{1} T_{1} + F_{2} n_{2} T_{2}}{F_{1} n_{1} + F_{2} n_{2}}$

Similar Questions

Two moles of helium are mixed with $n$ moles of hydrogen. If $\frac{C_P}{C_V} = \frac{3}{2}$ for the mixture,then the value of $n$ is:

$14 \, g$ of $CO$ at $27^{\circ} C$ is mixed with $16 \, g$ of $O_2$ at $47^{\circ} C$. The temperature of the mixture is .......... $^{\circ} C$ (vibration mode neglected).

Four moles of hydrogen,two moles of helium and one mole of water vapour form an ideal gas mixture. $[C_v$ for hydrogen $= \frac{5}{2} R, C_v$ for helium $= \frac{3}{2} R, C_v$ for water vapour $= 3 R]$. What is the molar specific heat at constant pressure of the mixture?

$A$ mixture of hydrogen and oxygen has a volume of $2000 \; cm^{3}$,a temperature of $300 \; K$,a pressure of $100 \; kPa$,and a mass of $0.76 \; g$. The ratio of the number of moles of hydrogen to the number of moles of oxygen in the mixture is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module