Question:
The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ change adiabatically from $\left(P, ?\right)$ to $\left(P?
If $\frac{\rho'}{\rho}=32$, then $\frac{P '}{P}$ is
The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ change adiabatically from $\left(P, ?\right)$ to $\left(P?
If $\frac{\rho'}{\rho}=32$, then $\frac{P '}{P}$ is
Updated On: Jul 7, 2022
- $\frac{1}{128}$
- $32$
- $128$
- $256$
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The Correct Option is C
Solution and Explanation
Here, $\gamma=\frac{7}{5}, P_{1}=P, \rho_{1}=\rho; P_{2}=P', \rho_{2}=\rho'$
For an adiabatic process, $PV^{\gamma} =$ constant
$\therefore P_{1}V_{1}^{\gamma }=P_{2}V_{2}^{\gamma}$
$\frac{P_{2}}{P_{1}}=\left(\frac{V_{1}}{V_{2}}\right)^{\gamma}=\left(\frac{\rho_{2}}{\rho_{1}}\right)^{\gamma}=\left(\frac{\rho'}{\rho}\right)^{7/5}=\left(32\right)^{7/5}$
$\frac{P'}{P}=\left(2^{5}\right)^{7/5}=2^{7}=128$
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Concepts Used:
Pressure
Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Everyday examples of pressure are:
- The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
- Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.
Formula:
When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:
P = F / A
Units of Pressure:
The SI unit of pressure is the pascal (Pa)
A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.