The ratio of two specific heats of gas Cₚ/Cᵥ / for argon is1.6 and for hydrogen is 1.4. Adiabatic elasticity of argon at pressure P is E. Adiabatic elasticity of hydrogen will also be equal to E at the pressure

To find the pressure at which the adiabatic elasticity of hydrogen is equal to the adiabatic elasticity of argon, we can use the formula for the adiabatic bulk modulus (elasticity) of a gas.

The adiabatic elasticity (bulk modulus) of a gas is given by the relation:
$E=\gamma P$
where:
• $\gamma$ is the ratio of specific heats ($C_p/C_v$)
• $P$ is the pressure of the gas.

Let us write the given values from the problem:
For argon:
�� Ratio of specific heats, ${\gamma }_{\text{Ar}}=1.6=\frac{8}{5}$
• Pressure, $P_{\text{Ar}}=P$
• Adiabatic elasticity, $E_{\text{Ar}}=E$

Therefore, for argon, we have:
$E={\gamma }_{\text{Ar}}{P}_{\text{Ar}}=1.6P=\frac{8}{5}P$

For hydrogen:
• Ratio of specific heats, ${\gamma }_{{\text{H}}_2}=1.4=\frac{7}{5}$
• Let the pressure of hydrogen be $P_{{\text{H}}_2}$ when its adiabatic elasticity is also equal to $E$.

Therefore, for hydrogen, we have:
$E={\gamma }_{{\text{H}}_2}{P}_{{\text{H}}_2}=1.4P_{{\text{H}}_2}=\frac{7}{5}{P}_{{\text{H}}_2}$

Since the adiabatic elasticity for both gases is equal to $E$, we can equate the two expressions:
$\frac{8}{5}P=\frac{7}{5}{P}_{{\text{H}}_2}$

Solving for $P_{{\text{H}}_2}$:
$P_{{\text{H}}_2}=\frac{8}{7}P$

Thus, the adiabatic elasticity of hydrogen will also be equal to $E$ at a pressure of $\frac{8P}{7}$.