- Home
- Standard 11
- Physics
The initial pressure and volume of an ideal gas are $P_0$ and $V_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{ V _0}{4}$ will be (Given $\gamma=$ ratio of specific heats at constant pressure and at constant volume)
$P _0(4)^{\frac{1}{\gamma}}$
$P _0(4)^\gamma$
$P _0$
$4 P _0$
Solution
As gas is suddenly compressed, the processes is adiabatic.
Equation of gas for adiabatic process is
$PV ^\gamma=\text { constant. }$
$\Rightarrow P _1 V _1^\gamma= P _2 V _2^\gamma$
$\Rightarrow P _0 V _0^\gamma= P _2\left(\frac{ V _0}{4}\right)^\gamma$
$\Rightarrow P _2= P _0(4)^\gamma$
Similar Questions
Match the thermodynamic processes taking place in a system with the correct conditions. In the table: $\Delta Q$ is the heat supplied, $\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system
| Process | Condition |
| $(I)$ Adiabatic | $(A)\; \Delta W =0$ |
| $(II)$ Isothermal | $(B)\; \Delta Q=0$ |
| $(III)$ Isochoric | $(C)\; \Delta U \neq 0, \Delta W \neq 0 \Delta Q \neq 0$ |
| $(IV)$ Isobaric | $(D)\; \Delta U =0$ |
