N_1 molecules of a gas at temperature T_1 are | vedclass

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

Question

(C) The total internal energy of the mixture is the sum of the internal energies of the individual gases.For a gas,the internal energy is given by $U

Vedclass · Accepted Answer

$\frac{(N_1 T_1 + N_2 T_2)}{(N_1 + N_2)}$

Vedclass · Answer

(C) The total internal energy of the mixture is the sum of the internal energies of the individual gases.For a gas,the internal energy is given by $U = \frac{3}{2} N k T$.Total internal energy $U_{total} = U_1 + U_2 = \frac{3}{2} N_1 k T_1 + \frac{3}{2} N_2 k T_2$.Let the final temperature of the mixture be $T$. The total internal energy of the mixture is $U_{final} = \frac{3}{2} (N_1 + N_2) k T$.By the law of conservation of energy,$U_{total} = U_{final}$.$\frac{3}{2} N_1 k T_1 + \frac{3}{2} N_2 k T_2 = \frac{3}{2} (N_1 + N_2) k T$.Canceling the common factor $\frac{3}{2} k$ from both sides:$N_1 T_1 + N_2 T_2 = (N_1 + N_2) T$.Therefore,the resulting temperature is $T = \frac{N_1 T_1 + N_2 T_2}{N_1 + N_2}$.

$N_1$ molecules of a gas at temperature $T_1$ are mixed with $N_2$ molecules at temperature $T_2$. The resulting temperature of the mixture gas is

Similar Questions

Four moles of hydrogen,two moles of helium,and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of the mixture?

The molar specific heat of a mixture at constant volume,if one mole of $He$ gas is mixed with three moles of $O_2$ gas,is: (in $R$)

$22 \ g$ of carbon dioxide at $27^{\circ} C$ is mixed in a closed container with $16 \ g$ of oxygen at $37^{\circ} C$. If both gases are considered as ideal gases,then the temperature of the mixture is nearly: (in $^{\circ} C$)

$A$ cylinder consists of a gas mixture of helium and oxygen. If the mass of helium is $4 \,g$ and the mass of oxygen is $32 \,g$, then the ratio of specific heat of the mixture $\left(C_p / C_V\right)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module