An ideal gas of volume V and pressure P expands isothermally to volume 16 V and then compressed adiabatically to volume V. The final pressure of gas is [γ=1.5]

Question

An ideal gas of volume V and pressure P expands isothermally to volume 16 V and then compressed adiabatically to volume V. The final pressure of gas is [&gamma;=1.5] (A) P (B) 3P (C) 4P (D) 6P

Tardigrade Admin · Accepted Answer

Isothermal expansion P1 V1=P2 V2 P V=16 V × P' (P/16)=P' P1 V1&gamma;=P2 V2&gamma; [adiabatic compression] P(16 V)1.5=P''(V)1.5 (P/16) × 161.5=P''=4 P

Q. An ideal gas of volume $V$ and pressure $P$ expands isothermally to volume $16 V$ and then compressed adiabatically to volume $V$ . The final pressure of gas is $[γ = 1.5]$

P

3P

4P

6P

Isothermal expansion
$P_{1} V_{1} = P_{2} V_{2}$
$P V = 16 V \times P^{'}$
$\frac{P}{16} = P^{'}$
$P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
[adiabatic compression]
$P (16 V)^{1.5} = P^{''} (V)^{1.5}$
$\frac{P}{16} \times 1 6^{1.5} = P^{''} = 4 P$

Q. An ideal gas of volume V and pressure P expands isothermally to volume 16V and then compressed adiabatically to volume V. The final pressure of gas is [γ=1.5]

P

3P

4P

6P

Isothermal expansion P1​V1​=P2​V2​ PV=16V×P′ 16P​=P′ P1​V1γ​=P2​V2γ​ [adiabatic compression] P(16V)1.5=P′′(V)1.5 16P​×161.5=P′′=4P

Q. An ideal gas of volume $V$ and pressure $P$ expands isothermally to volume $16 V$ and then compressed adiabatically to volume $V$ . The final pressure of gas is $[γ = 1.5]$

Isothermal expansion
$P_{1} V_{1} = P_{2} V_{2}$
$P V = 16 V \times P^{'}$
$\frac{P}{16} = P^{'}$
$P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$
[adiabatic compression]
$P (16 V)^{1.5} = P^{''} (V)^{1.5}$
$\frac{P}{16} \times 1 6^{1.5} = P^{''} = 4 P$