Let the final temperature of the mixture be T.
Since, there is no loss in energy.
ΔU=0
⇒2F1n1RΔT+2F2n2RΔT=0
⇒2F1n1R(T1−T)+2F2n2R(T2−T)=0
⇒T=F1n1R+F2n2RF1n1RT1+F2n2RT2=F1n1+F2n2F1n1T1+F2n2T2
Two ideal polyatomic gases at temperatures T1 and T2 are mixed so that there is no loss of energy. If F1 and F2,m1 and m2,n1 and n2 be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is:
Held on 17 Mar 2021 · Verified 6 Jul 2026.
n1+n2n1T1+n2T2
n1F1+n2F2n1F1T1+n2F2T2
F1+F2n1F1T1+n2F2T2
n1+n2n1F1T1+n2F2T2
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same $P, V, T$. Heating is started from left side until pressure changes to $\dfrac{27P}{8}$. If initial volume of each compartment was $9$ litres then the final volume in right-hand side compartment is __________ litres. (for this ideal gas $C_P/C_V = 1.5$)
A gas based geyser heats water flowing at the rate of 5.0 litres per minute from $27^{\circ} \mathrm{C}$ to $87^{\circ} \mathrm{C}$. The rate of consumption of the gas is $\_\_\_\_$ $\mathrm{g} / \mathrm{s}$. (Take heat of combustion of gas $=5.0 \times 10^{4} \mathrm{~J} / \mathrm{g}$) specific heat capacity of water $=4200 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$
The internal energy of a monoatomic gas is 3 nRT. One mole of helium is kept in a cylinder having internal cross section area of $17 \mathrm{~cm}^{2}$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by $4^{\circ} \mathrm{C}$, then the piston will move $\_\_\_\_$ cm. (atmospheric pressure $=10^{5} \mathrm{~Pa}$)
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: If the average kinetic energy of $H_2$ and $O_2$ molecules, kept in two different sized containers are same, then their temperatures will be same. Reason R: The r.m.s. speed of $H_2$ and $O_2$ molecules are same at same temperature. Choose the correct answer from the options given below
Consider two boxes containing ideal gases $A$ and $B$ such that their temperatures, pressures and number densities are same. The molecular size of $A$ is half of that of $B$ and mass of molecule $A$ is four times that of $B$. If the collision frequency in gas $B$ is $32 \times 10^{18} / \mathrm{s}$ then collision frequency in gas $A$ is $\_\_\_\_$ $/ \mathrm{s}$.
Work through every JEE Main Thermodynamics PYQ, year by year.