In an adiabatic process,the density of a diat | vedclass

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

Question

(D) For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $PV^{\gamma} = 	ext{constant}$.Since density $ho = \frac{

Vedclass · Accepted Answer

$128$

Vedclass · Answer

(D) For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $PV^{\gamma} = 	ext{constant}$.Since density $ho = \frac{m}{V}$,we have $V = \frac{m}{ho}$.Substituting this into the adiabatic equation: $P \left(\frac{m}{ho}ight)^{\gamma} = 	ext{constant}$.Since mass $m$ is constant,we get $P \propto ho^{\gamma}$.Therefore,$\frac{P_f}{P_i} = \left(\frac{ho_f}{ho_i}ight)^{\gamma}$.For a diatomic gas,the adiabatic index $\gamma = \frac{7}{5} = 1.4$.Given $ho_f = 32 ho_i$,we have $\frac{ho_f}{ho_i} = 32$.Thus,$n = \frac{P_f}{P_i} = (32)^{7/5} = (2^5)^{7/5} = 2^7 = 128$.

In an adiabatic process,the density of a diatomic gas becomes $32$ times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is

Similar Questions

The bulk modulus of a gas is defined as $B = -V (dp / dV)$. For an adiabatic process,the variation of $B$ is proportional to $p^n$. For an ideal gas,$n$ is:

$A$ gas at $NTP$ is suddenly compressed to one-fourth of its original volume. If $\gamma$ is supposed to be $\frac{3}{2}$,then the final pressure is........ atmosphere.

$200 \ cc$ of an ideal gas $(\gamma = 1.5)$ expands adiabatically. If the rms speed of the gas molecules becomes half of the initial value,the final volume of the gas is (in $cc$)

An ideal gas,undergoing adiabatic change,has which of the following pressure-temperature relationships?

During an adiabatic compression,$830 \ J$ of work is done on $2 \ moles$ of a diatomic ideal gas to reduce its volume by $50\%$. The change in its temperature is nearly..... $K$ $(R = 8.3 \ J \ K^{-1} \ mol^{-1})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module