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

Question

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

Tardigrade Admin · Accepted Answer

In the isothermal process PV = constant ∴ P d V+V d P=0 or (( d P/ d V))=-((P/V)) ∴ Bulk modulus, B=-(( d P/ d V / V))=-(( d P/ d V)) V ∴ B=-[(-(P/V)) V]=P ∴ B=P Note: Adiabatic bulk modulus is given by B=&gamma; P

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

$\frac{2}{3} P$

$P$

$\frac{3}{2} P$

$2 P$

In the isothermal process
$P V =$ constant
$∴ P d V + V d P = 0$ or $(\frac{d P}{d V}) = - (\frac{P}{V})$
$∴$ Bulk modulus, $B = - (\frac{d P}{d V / V}) = - (\frac{d P}{d V}) V$
$∴ B = - [(- \frac{P}{V}) V] = P$
$∴ B = P$
Note: Adiabatic bulk modulus is given by $B = γ P$

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

32​P

P

23​P

2P

In the isothermal process PV= constant ∴PdV+VdP=0 or (dVdP​)=−(VP​) ∴ Bulk modulus, B=−(dV/VdP​)=−(dVdP​)V ∴B=−[(−VP​)V]=P ∴B=P Note: Adiabatic bulk modulus is given by B=γP

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

$\frac{2}{3} P$

$P$

$\frac{3}{2} P$

$2 P$

In the isothermal process
$P V =$ constant
$∴ P d V + V d P = 0$ or $(\frac{d P}{d V}) = - (\frac{P}{V})$
$∴$ Bulk modulus, $B = - (\frac{d P}{d V / V}) = - (\frac{d P}{d V}) V$
$∴ B = - [(- \frac{P}{V}) V] = P$
$∴ B = P$
Note: Adiabatic bulk modulus is given by $B = γ P$