Question

(i) Prove that the isothermal elasticity of a gas is equal to its pressure.
(ii) Prove that the adiabatic elasticity of the gas = yx P, where P is
pressure of the gas and y =C,1C.,C, and C, being the specific heats
of the gas at constant pressure and constant volume respectively. (5)​

Answer 1

Answer:

Correct option is

A

Final pressure

The isothermal elasticity is given by

E

iso

=

volumestrain

volumestress

=

−

V

ΔV

Δp

[∵Δp=

A

F

]

⇒E

iso

=−V(

ΔV

Δp

).

Minus sign indicates decrease in volume due to increase in pressure.

From ideal gas equation

pV=RT

At constant temperature

pV= constant

∴pΔV+VΔp=0

∴V(

ΔV

Δp

)=−p

∴E

iso

=−V(

ΔV

−Δp

)=−(−p)=p

= Final pressure.