Question

Adiabatic modulus of elasticity of a gas is $2.1\times {10}^{5}N{m}^{-2}$. It's isothermal modulus of elasticity is ($\gamma =1.4$)

• A. $1.2\times {10}^{5}N{m}^{-2}$
• B. $1.4\times {10}^{5}N{m}^{-2}$
• C. $1.5\times {10}^{5}N{m}^{-2}$
• D. $1.8\times {10}^{5}N{m}^{-2}$

Answer 1

The correct option is C $1.5\times {10}^{5}N{m}^{-2}$

Adiabatic bulk modulus of a gas $K_S=\gamma P$
Isothermal bulk modulus $K_T=P$
$\frac{K_S}{K_T}=\frac{\gamma P}{P}=\gamma =\frac{C_p}{C_v}$
$\frac{2.1\times {10}^5}{K_T}=1.4$
$K_T=\frac{2.1\times {10}^5}{1.4}=1.5\times {10}^5$
Option C.