During an experiment,an ideal gas is found to | vedclass

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

Question

(D) Given condition: $\frac{P^2}{ho} = 	ext{constant}$.From the ideal gas equation,$P = \frac{ho RT}{M}$,so $ho = \frac{PM}{RT}$.Substituting $

Vedclass · Accepted Answer

Both $(B)$ and $(C)$.

Vedclass · Answer

(D) Given condition: $\frac{P^2}{ho} = 	ext{constant}$.From the ideal gas equation,$P = \frac{ho RT}{M}$,so $ho = \frac{PM}{RT}$.Substituting $ho$ into the given condition: $\frac{P^2}{PM/RT} = \frac{PRT}{M} = 	ext{constant}$.Since $R$ and $M$ are constants,$PT = 	ext{constant}$.This represents a rectangular hyperbola on a $P-T$ diagram,so statement $(C)$ is correct.Now,for the expansion where $ho_2 = ho/2$:Using $\frac{P_1^2}{ho_1} = \frac{P_2^2}{ho_2} \Rightarrow \frac{P^2}{ho} = \frac{P_2^2}{ho/2} \Rightarrow P_2^2 = \frac{P^2}{2} \Rightarrow P_2 = \frac{P}{\sqrt{2}}$.Using $P_1 T_1 = P_2 T_2$ (since $PT = 	ext{constant}$):$PT = \left(\frac{P}{\sqrt{2}}ight) T_2 \Rightarrow T_2 = \sqrt{2} T$.Thus,statement $(B)$ is also correct.Therefore,the correct option is $(D)$.

During an experiment,an ideal gas is found to obey a condition $\frac{P^2}{\rho} = \text{constant}$ [$\rho = \text{density of the gas}$]. The gas is initially at temperature $T$,pressure $P$,and density $\rho$. The gas expands such that density changes to $\rho/2$.

Similar Questions

For the equation $\beta = - \frac{1}{V} \left( \frac{dV}{dP} \right)$, identify the correct graph of $\beta$ versus $P$ for an ideal gas at constant temperature.

Which of the following statements about the kinetic theory of gases is wrong?

Statement-$1$: Internal energy of a gas $U = nC_VT$ is due to the random motion of gas molecules.
Statement-$2$: $A$ container is moving with speed $v$. It is suddenly stopped by a force,and the temperature of the gas increases.

$A$ 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 $R = 8.32\,J\,mol^{-1}K^{-1}$)

An insulated container containing a monoatomic gas of molar mass $M$ is moving with a velocity $V_{0}$. If the container is suddenly stopped,find the change in temperature.

Vedclass Test Series

Exam Paper Generator

Online Exam Module