A monoatomic gas pressure P-1 and volume V-1 is compressed adiabatically to displaystyle frac-1-8-th of its original volume- What is the final pressure of the gasP-164P-116P-132P-1

Question

Toppr Admin · Accepted Answer

Ideal gas equation- for an adiabatic process isPV-x3B3- constant -xA0- -xA0- or -xA0- -xA0- P1V-x3B3-1-P2V-x3B3-2For monoatomic gas -x3B3-53P1V5-31-P2-V18-5-3-x21D2-P2-P1-xD7-2-5-32P1

A monoatomic gas at pressure $P_{1}$ and volume $V_{1}$ is compressed adiabatically to $\frac{1}{8}$ th of its original volume. What is the final pressure of the gas
$P_{1}$
$64 P_{1}$
$16 P_{1}$
$32 P_{1}$

Ideal gas equation, for an adiabatic process is
$P V^{γ} =$ constant or $P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
For monoatomic gas $γ = \frac{5}{3}$
$P_{1} V_{1}^{5 / 3} = P_{2} {(\frac{V_{1}}{8})}^{5 / 3}$
$\Rightarrow P_{2} = P_{1} \times (2)^{5} = 32 P_{1}$

A monoatomic gas at pressure P1 and volume V1 is compressed adiabatically to 18th of its original volume. What is the final pressure of the gasP164P116P132P1

Ideal gas equation, for an adiabatic process isPVγ= constant or P1Vγ1=P2Vγ2For monoatomic gas γ=53P1V5/31=P2(V18)5/3⇒P2=P1×(2)5=32P1

A monoatomic gas at pressure $P_{1}$ and volume $V_{1}$ is compressed adiabatically to $\frac{1}{8}$ th of its original volume. What is the final pressure of the gas
$P_{1}$
$64 P_{1}$
$16 P_{1}$
$32 P_{1}$

Ideal gas equation, for an adiabatic process is
$P V^{γ} =$ constant or $P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
For monoatomic gas $γ = \frac{5}{3}$
$P_{1} V_{1}^{5 / 3} = P_{2} {(\frac{V_{1}}{8})}^{5 / 3}$
$\Rightarrow P_{2} = P_{1} \times (2)^{5} = 32 P_{1}$