A cylinder with a movable piston contains 3,moles of hydrogen at standard temperature and pressure.

English

Gujarati

Hindi

11.Thermodynamics

easy

A cylinder with a movable piston contains $3\,moles$ of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increases if the gas is compressed to half its original volume?

A

$(2)^{7 / 5}$

B

$(2)^{1 / 5}$

C

$(5)^{7 / 5}$

D

$(2)^{1 / 5}$

Solution

(a)

The process is adiabatic

$\therefore P _1 V _1^\gamma= P _2 V _2^\gamma$

Given, $\frac{ V _1}{ V _2}=\frac{2}{1}$ and $\gamma=\frac{7}{5}$ (for diatomic gas)

$\therefore \frac{ P _2}{ P _1}=(2)^{7 / 5} \quad \text { i.e., } P _2=(2)^{7 / 5} P _1$

Standard 11

Physics

Share

Similar Questions

Check the statement are trrue or false :

$1.$ The change in internal energy $\Delta U = 0$ in a cyclic process.

$2.$ In an adiabatic process temperature remains constant.

$3.$ The internal energy of a system during isothermal process decreases.

medium

A sample of $1$ mole gas at temperature $\mathrm{T}$ is adiabatically expanded to double its volume. If adiabatic constant for the gas is $\gamma=\frac{3}{2}$, then the work done by the gas in the process is:

hard

(JEE MAIN-2024)

One mole of an ideal gas with $\gamma = 1.4$, is adiabatically compressed so that its temperature rises from $27°C$ to $35°C$. The change in the internal energy of the gas is ……. $J$ $(R = 8.3\,J/mol.K)$

medium

The work done in which of the following processes is equal to the internal energy of the system?

easy

(AIIMS-2017)

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in$P-V$ diagram. The relation between the ratio $\frac{V_a}{V_d}$ and the ratio $\frac{V_b}{V_c}$ is:

hard

(JEE MAIN-2024)