An ideal gas expands adiabatically, (gamma = | vedclass

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

Question

(A) The r.m.s. velocity of gas molecules is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms} \propto \sqrt{T}$, reducing the $v_{rms}$ by a fa

Vedclass · Accepted Answer

$256$

Vedclass · Answer

(A) The r.m.s. velocity of gas molecules is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$.Since $v_{rms} \propto \sqrt{T}$, reducing the $v_{rms}$ by a factor of $4$ means the temperature $T$ must be reduced by a factor of $4^2 = 16$.So, $T_f = \frac{T_i}{16}$.For an adiabatic process, the relationship between temperature and volume is $TV^{\gamma-1} = 	ext{constant}$.Thus, $T_i V_i^{\gamma-1} = T_f V_f^{\gamma-1}$.Substituting the values, $T_i V_i^{1.5-1} = \frac{T_i}{16} V_f^{1.5-1}$.$V_i^{0.5} = \frac{1}{16} V_f^{0.5}$.$\sqrt{V_i} = \frac{1}{16} \sqrt{V_f}$.$\sqrt{\frac{V_f}{V_i}} = 16$.$\frac{V_f}{V_i} = 16^2 = 256$.Therefore, the gas must be expanded $256$ times.

An ideal gas expands adiabatically, $(\gamma = 1.5)$. To reduce the root-mean-square (r.m.s.) velocity of the molecules $4$ times, the gas has to be expanded by a factor of: (in $\times$)

Similar Questions

An ideal gas at $27 \, ^\circ C$ is compressed adiabatically such that its volume becomes $8/27$ of its original volume. If $\gamma = 5/3$ for the gas,the increase in temperature of the gas is ..... $K$.

An ideal rigid diatomic gas $(\gamma = 7/5)$ undergoes an adiabatic change. If the relation between temperature and volume is $TV^x = \text{constant}$, then the value of $x$ is:

$A$ polyatomic gas $(\gamma = 4/3)$ is compressed to $(1/8)^{\text{th}}$ of its initial volume adiabatically. If its initial pressure is $P_0$,what will be its new pressure (in $P_0$)?

In adiabatic compression, the decrease in volume is associated with

Which of the following is true in the case of an adiabatic process, where $\gamma = C_p / C_V$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module