A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be:

Question

A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be: (A) P (B) 8 P (C) 32 P (D) 64 P

Tardigrade Admin · Accepted Answer

Constant entropy means process is adiabatic PV &gamma;= constant V 2=( V 1/8) P 1 V 1&gamma;= P 2 V 2&gamma; P 1 V 1&gamma;= P 2(( V 1/8))5 / 3 P 1 V 15 / 3=( P 2 V 15 / 3/32) P 2=32 P 1

Q. A monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be:

$P$

$8 P$

$32 P$

$64 P$

Constant entropy means process is adiabatic
$P V^{γ} =$ constant
$V_{2} = \frac{V _{1}}{8}$
$P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
$P_{1} V_{1}^{γ} = P_{2} (\frac{V _{1}}{8})^{5/3}$
$P_{1} V_{1}^{5/3} = \frac{P _{2} V _{1}^{5/3}}{32}$
$P_{2} = 32 P_{1}$

Q. A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be:

P

8P

32P

64P

Constant entropy means process is adiabatic PVγ= constant V2​=8V1​​ P1​V1γ​=P2​V2γ​ P1​V1γ​=P2​(8V1​​)5/3 P1​V15/3​=32P2​V15/3​​ P2​=32P1​

Q. A monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be:

$P$

$8 P$

$32 P$

$64 P$

Constant entropy means process is adiabatic
$P V^{γ} =$ constant
$V_{2} = \frac{V _{1}}{8}$
$P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
$P_{1} V_{1}^{γ} = P_{2} (\frac{V _{1}}{8})^{5/3}$
$P_{1} V_{1}^{5/3} = \frac{P _{2} V _{1}^{5/3}}{32}$
$P_{2} = 32 P_{1}$