Question

Assertion :Ratio of isothermal bulk modulus and adiabatic bulk modulus for a monoatomic gas at a gIven pressure is $\frac{3}{5}$ Reason: This ratio is equal to $\gamma =\frac{C_p}{C_v}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is correct but Reason is incorrect

Due to high compressibility, gases possess volume elasticity. However, the magnitude of the volume elasticity depends on conditions under which it is compressed.

If the gas is compressed such that the temperature is not allowed to change, i.e. under isothermal conditions than the corresponding volume elasticity is known as isothermal elasticity represented as KT.

If the gas is compressed such that no heat is allowed to enter or leave the system, i.e. under adiabatic conditions than the corresponding elasticity is known as adiabatic elasticity and is represented as KΦ.

For isothermal bulk modulus: For a perfect gas at constant temperature,

pV = constant

Differentiating the above, we get,

p+ V$\frac{dp}{dV}$ = 0

p = -$\frac{dp}{dV/V}$ which is measure of volume elasticity

Under isothermal conditions

K${}_T$ = p

For adiabatic elasticity:

pVγ = constant

By differentiating we get, K${}_{\varphi }$ = yp

where y =$\frac{C_v}{C_p}$

Hence assertion is correct but the Reason is incorrect