Question

In an isentropic process, the pressure of a monoatomic ideal gas increases by 0.5%. The volume will decrease (in %) by (Take (0.995)^0.625= 0.997):

1. 0.4
2. 0.3
3. 0.2
4. 0.1

Answer 1

Correct Answer - Option 2 : 0.3

Concept:

For the isentropic process the relation is,

PV^γ  = Constant

Calculation:

Given:

Pressure increased = 0.5%, So P₂ = 1.005 P₁

For monoatomic γ  = 1.667

P₁V₁^1.667 = P₂V₂^1.667

P₁V₁^1.667 = 1.005 P₁ V₂^1.667

^{\(\frac{{{P_1}}}{{1.005{P_1}}} = {\left( {\frac{{{V_2}}}{{{V_1}}}} \right)^{1.667}}\)}

\({\left( {\frac{1}{{1.005}}} \right)^{\frac{1}{{1.667}}}} = \left( {\frac{{{V_2}}}{{{V_1}}}} \right)\)

(0.995)^0.6 × V₁ = V₂

0.997 V₁ = V₂

V₂ = 99.7 % of V₁

The volume will decrease 0.3%.