A monoatomic gas is filled in a cylindrical c | vedclass

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

Question

(D) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by $T V^{\gamma - 1} = 	ext{constant}$.Thus,$T_1 V_1^{\

Vedclass · Accepted Answer

$(\frac{L_2}{L_1})^{2/3}$

Vedclass · Answer

(D) For an adiabatic process,the relationship between temperature $T$ and volume $V$ is given by $T V^{\gamma - 1} = 	ext{constant}$.Thus,$T_1 V_1^{\gamma - 1} = T_2 V_2^{\gamma - 1}$,which implies $\frac{T_1}{T_2} = (\frac{V_2}{V_1})^{\gamma - 1}$.Since the container is cylindrical with cross-sectional area $A$,the volume $V$ can be expressed as $V = L 	imes A$,where $L$ is the length of the gas column.Therefore,$\frac{V_2}{V_1} = \frac{L_2 A}{L_1 A} = \frac{L_2}{L_1}$.For a monoatomic gas,the adiabatic index $\gamma = 5/3$.Substituting these values,we get $\frac{T_1}{T_2} = (\frac{L_2}{L_1})^{5/3 - 1} = (\frac{L_2}{L_1})^{2/3}$.

$A$ monoatomic gas is filled in a cylindrical container with a piston at temperature $T_1$. It undergoes an adiabatic expansion such that its temperature becomes $T_2$. If $L_1$ and $L_2$ are the lengths of the gas column before and after the expansion respectively,then $T_1/T_2$ is equal to:

Similar Questions

The pressure and density of a diatomic gas $(\gamma = 7/5)$ change adiabatically from $(P, d)$ to $(P', d')$. If $\frac{d'}{d} = 32$,then $\frac{P'}{P}$ is equal to:

In an adiabatic process,the state of a gas is changed from $(P_1, V_1, T_1)$ to $(P_2, V_2, T_2)$. Which of the following relations is correct?

One mole of nitrogen gas being initially at a temperature of $T_0 = 300 \,K$ is adiabatically compressed to increase its pressure $10$ times. The final gas temperature after compression is (Assume, nitrogen gas molecules as rigid diatomic and $100^{1/7} = 1.9$) (in $\,K$)

$A$ polyatomic gas $\left( \gamma = \frac{4}{3} \right)$ is compressed to $\frac{1}{8}$ of its volume adiabatically. If its initial pressure is $P_0$,its new pressure will be (in $P_0$)

In a thermodynamic system,$W$ represents the work done by the system and $\Delta U$ is the increase in internal energy. Which of the following statements is $TRUE$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module