A given quantity of an ideal gas is at the pressure P and the absolute temperature T . The isothermal bulk modulus of the gas is

Question

A given quantity of an ideal gas is at the pressure P and the absolute temperature T . The isothermal bulk modulus of the gas is (A) (2/3)P (B) P (C) (3/2)P (D) 2P

Tardigrade Admin · Accepted Answer

∵ β =(Δ P/(Δ V)V) ∴ In the isothermal process (P + Δ P) (V - Δ V)=PV or PV-PΔ V+VΔ P-Δ PΔ V=PV But Δ P Δ V maybe neglected. ∴ V Δ P=P Δ V or (Δ P/(Δ V)V)=P Hence, ( P ) is correct.

Q. A given quantity of an ideal gas is at the pressure $P$ and the absolute temperature $T$ . The isothermal bulk modulus of the gas is

$\frac{2}{3} P$

$P$

$\frac{3}{2} P$

$2 P$

$∵$ $β = \frac{Δ P}{\frac{Δ V}{V}}$
$∴$ In the isothermal process $(P + Δ P) (V - Δ V) = P V$
or $P V - P Δ V + V Δ P - Δ P Δ V = P V$
But $Δ P Δ V$ maybe neglected.
$∴$ $V Δ P = P Δ V$
or $\frac{Δ P}{\frac{Δ V}{V}} = P$
Hence, ( $P$ ) is correct.

Q. A given quantity of an ideal gas is at the pressure P and the absolute temperature T . The isothermal bulk modulus of the gas is

32​P

P

23​P

2P

∵ β=VΔV​ΔP​ ∴ In the isothermal process (P+ΔP)(V−ΔV)=PV or PV−PΔV+VΔP−ΔPΔV=PV But ΔPΔV maybe neglected. ∴ VΔP=PΔV or VΔV​ΔP​=P Hence, ( P ) is correct.

Q. A given quantity of an ideal gas is at the pressure $P$ and the absolute temperature $T$ . The isothermal bulk modulus of the gas is

$\frac{2}{3} P$

$P$

$\frac{3}{2} P$

$2 P$

$∵$ $β = \frac{Δ P}{\frac{Δ V}{V}}$
$∴$ In the isothermal process $(P + Δ P) (V - Δ V) = P V$
or $P V - P Δ V + V Δ P - Δ P Δ V = P V$
But $Δ P Δ V$ maybe neglected.
$∴$ $V Δ P = P Δ V$
or $\frac{Δ P}{\frac{Δ V}{V}} = P$
Hence, ( $P$ ) is correct.