Gas obey P^2V = constant. initial temperature and volume are T_0 and V_0 . If gas expands to volume

English

Gujarati

Hindi

11.Thermodynamics

normal

Gas obey $P^2V =$ constant. The initial temperature and volume are $T_0$ and $V_0$. If gas expands to volume $2V_0$, its final temperature becomes

A

$\sqrt 2 {T_0}$

B

$2T_0$

C

$T_0/2$

D

${T_0}/\sqrt 2 $

Solution

$\mathrm{P}^{2} \mathrm{V}=\mathrm{constant}$

$\left(\frac{\mathrm{nRT}}{\mathrm{V}}\right)^{2} \mathrm{V}=\mathrm{constant} ; \frac{\mathrm{T}^{2}}{\mathrm{V}}=\mathrm{constant}$

$\frac{\mathrm{T}_{1}^{2}}{\mathrm{V}_{1}}=\frac{\mathrm{T}_{2}^{2}}{\mathrm{V}_{2}}$

$\frac{\mathrm{T}^{2}}{\mathrm{V}_{0}}=\frac{\mathrm{T}_{2}^{2}}{2 \mathrm{V}_{0}} \Rightarrow\left(\mathrm{T}_{2}=\sqrt{2} \mathrm{T}_{0}\right)$

Standard 11

Physics

Share

Similar Questions

In an adiabatic expansion the product of pressure and volume.

normal

$1\ cc$ of water at its boiling point $(100^o\ C)$ is converted into steam by supplying it $540\ calories$ of heat the volume of steam is $1671\ cc$. If atmospheric pressure is $1.013 × 10^ 5\ Nm^{-2}$ and $J = 4.18\ joule/cal$ the approximate value of heat that is required in overcoming the molecular attraction is …….. $cal$

normal

In an adiabatic expansion of a gas initial and final temperatures are ${T_1}$ and ${T_2}$ respectively, then the change in internal energy of the gas is

normal

A student records $\Delta Q,\Delta U$ and $\Delta W$ for a thermodynamic cycle $A \to B \to C \to A.$ Certain entries are missing. Find correct entry in following options

$AB$ $BC$ $CA$

$\Delta W$ $40\,J$ $30\,J$

$\Delta U$ $50\,J$

$\Delta Q$ $150\,J$ $10\,J$

normal

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$ . The total work done is $W$ . Then

normal