Three ideal gases at absolute temperatures T_ | vedclass

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

Question

(D) For an ideal gas,the average kinetic energy per molecule is given by $K.E. = \frac{3}{2} k_B T$ (assuming monatomic gas for simplicity,though the

Vedclass · Accepted Answer

$\frac{n_1T_1 + n_2T_2 + n_3T_3}{n_1 + n_2 + n_3}$

Vedclass · Answer

(D) For an ideal gas,the average kinetic energy per molecule is given by $K.E. = \frac{3}{2} k_B T$ (assuming monatomic gas for simplicity,though the factor cancels out). The total internal energy of $n$ molecules is $U = n 	imes (\frac{3}{2} k_B T)$.Since there is no loss of energy,the total internal energy of the mixture is the sum of the internal energies of the individual gases:$U_{total} = U_1 + U_2 + U_3$$(n_1 + n_2 + n_3) 	imes (\frac{3}{2} k_B T) = n_1 (\frac{3}{2} k_B T_1) + n_2 (\frac{3}{2} k_B T_2) + n_3 (\frac{3}{2} k_B T_3)$Canceling the common factor $\frac{3}{2} k_B$ from both sides:$(n_1 + n_2 + n_3) T = n_1 T_1 + n_2 T_2 + n_3 T_3$Therefore,the final temperature $T$ is:$T = \frac{n_1 T_1 + n_2 T_2 + n_3 T_3}{n_1 + n_2 + n_3}$

Three ideal gases at absolute temperatures $T_1, T_2,$ and $T_3$ are mixed. The number of molecules are $n_1, n_2,$ and $n_3$ respectively. Assuming no loss of energy,what is the final temperature of the mixture?

Similar Questions

If $2 \text{ mole}$ of an ideal monoatomic gas at temperature $T$ is mixed with $6 \text{ mole}$ of another ideal monoatomic gas at temperature $2T$, then the temperature of the mixture is:

$A$ gaseous mixture consists of $4 \ g$ oxygen and $4 \ g$ of helium. The ratio $\frac{C_p}{C_V}$ of the mixture is ($C_p$ and $C_V$ are molar specific heats of the mixture at constant pressure and at constant volume respectively).

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:

Find $\gamma$ for the mixture of $11 \, g$ of $CO_{2}$ and $14 \, g$ of $N_{2}$.

$A$ rigid tank contains $35 \, kg$ of nitrogen at $6 \, atm$. $A$ sufficient quantity of oxygen is supplied to increase the pressure to $9 \, atm$,while the temperature remains constant. The amount of oxygen supplied to the tank is .... $kg$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module