A certain amount of an ideal gas is contained | vedclass

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

Question

(B) Let $m$ be the total mass of the gas. The kinetic energy of the gas due to the motion of the vessel is $K = \frac{1}{2}mv^2$.When the vessel is su

Vedclass · Accepted Answer

$\frac{Mv^2(\gamma - 1)}{2R}$

Vedclass · Answer

(B) Let $m$ be the total mass of the gas. The kinetic energy of the gas due to the motion of the vessel is $K = \frac{1}{2}mv^2$.When the vessel is suddenly stopped,this kinetic energy is converted into the internal energy of the gas,causing a rise in temperature $\Delta T$.Using the relation for internal energy change,$\Delta U = \mu C_V \Delta T$,where $\mu = \frac{m}{M}$ is the number of moles.Equating the kinetic energy to the change in internal energy: $\frac{1}{2}mv^2 = \frac{m}{M} C_V \Delta T$.Since $C_V = \frac{R}{\gamma - 1}$,we substitute this into the equation:$\frac{1}{2}mv^2 = \frac{m}{M} \left( \frac{R}{\gamma - 1} \right) \Delta T$.Canceling $m$ from both sides and solving for $\Delta T$:$\Delta T = \frac{Mv^2(\gamma - 1)}{2R}$.

$A$ certain amount of an ideal gas is contained in a closed vessel. The vessel is moving with a constant velocity $v$. The molecular mass of the gas is $M$. What is the rise in temperature of the gas when the vessel is suddenly stopped? (Given $\gamma = C_P/C_V$)

Similar Questions

$A$ gas is filled in the cylinder shown in the figure. The two pistons are joined by a string. If the gas is heated,the pistons will

$A$ vessel contains $14\,g$ of nitrogen gas at a temperature of $27^{\circ}\,C$. The amount of heat to be transferred to the gas to double the r.m.s. speed of its molecules will be $......J$ (Take $R = 8.32\,J\,mol^{-1}K^{-1}$)

Two closed containers of equal volume are filled with air at pressure $P_0$ and temperature $T_0$. Both are connected by a narrow tube. If one of the containers is maintained at temperature $T_0$ and the other at temperature $T$,then the new pressure in the containers will be:

$A$ $15\,g$ mass of nitrogen gas is enclosed in a vessel at a temperature $27\,^{\circ}C.$ The amount of heat transferred to the gas,so that the rms velocity of the molecules is doubled,is about ...... $kJ$ [Take $R = 8.3\,J/K\,mole$ ]

According to the kinetic theory of gases,when two molecules of a gas collide with each other,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module