A gas is suddenly compressed to one fourth of | vedclass

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

Question

(B) For a sudden compression,the process is adiabatic. The adiabatic equation is $P V^{\gamma} = 	ext{constant}$.Let the initial pressure be $P_1 = P

Vedclass · Accepted Answer

More than $P$

Vedclass · Answer

(B) For a sudden compression,the process is adiabatic. The adiabatic equation is $P V^{\gamma} = 	ext{constant}$.Let the initial pressure be $P_1 = P$ and initial volume be $V_1 = V$.The final volume is $V_2 = V/4$.Using the relation $\frac{P_2}{P_1} = \left( \frac{V_1}{V_2} ight)^{\gamma}$,we get:$\frac{P_2}{P} = \left( \frac{V}{V/4} ight)^{\gamma} = 4^{\gamma}$.Therefore,$P_2 = 4^{\gamma} P$.Since the adiabatic index $\gamma$ for any gas is greater than $1$ (e.g.,$1.4$ for diatomic,$1.67$ for monatomic),$4^{\gamma}$ will be greater than $4$.Thus,$P_2 > 4P$,which means the final pressure is much more than $P$.

$A$ gas is suddenly compressed to one fourth of its original volume. What will be its final pressure,if its initial pressure is $P$?

Similar Questions

$A$ diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_0}{32}$,where $V_0$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is $xT_i$ in Kelvin. The value of $x$ is:

When a gas expands adiabatically, its volume is doubled while its absolute temperature is decreased by a factor of $2$. The value of the adiabatic constant $\gamma$ is

The relation between volume $(V)$ and absolute temperature $(T)$ of a gas in an adiabatic process is

$A$ mixture of gases at $STP$ for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{9}$th of its original volume. The final temperature of the mixture is .......... $^{\circ}C$.

An ideal gas at $127^{\circ} C$ is compressed suddenly to $\frac{8}{27}$ of its initial volume. If $\gamma=\frac{5}{3}$ for the ideal gas, then the rise in its temperature is: (in $K$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module