If the pressure of gas is increased from 1.01×10⁵ Pa to 1.165×10⁵ Pa and volume

If The Pressure Of Gas Is Increased From 101x10 Pa Physics QuestionIf The Pressure Of Gas Is Increased From 101x10 Pa Physics Question

If the pressure of gas is increased from 1.01×10⁵ Pa to 1.165×10⁵ Pa and volume is decreases by 10% at constant temperature then the bulk modulus of the gas is

Options

(a) 15.5×10⁵ Pa
(b) 1.4×10⁵ Pa
(c) 1.55×10⁵ Pa
(d) 0.0155×10⁵ Pa

Correct Answer:

1.55×10⁵ Pa

Explanation:

Bulk modulus = normal stress / volumetric strain
= (F/A) / (-∆V/V) = -(PV / ∆V)
For an isothermal process, PV = constant
So, PdV + VdP = 0 ⇒ (-VdP / dV) = P
B = (-VdP / dV) = (100 / 10) × (1.165 × 10⁵ – 1.01 × 10⁵)
= 1.55 × 10⁵ Pa.

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