Question

An ideal monoatomic gas obeys the law $P{V}^x$ = constant. For what value of x, it has negative molar specific heat :-

• A. x > 1.67
• B. x < 1.67
• C. 1 < x < 1.4
• D. 1 < x < 1.67

Answer 1

The correct option is D 1 < x < 1.67

Given : An ideal monoatomic gas obeys the law $P{V}^x$= constant. For what value of x, it has negative molar specific heat :

Solution :

Molar specific heat $C_v=\frac{R}{\gamma -1}+\frac{R}{1-x}$

Gas is monoatomic so $\gamma =1.67$

For negative molar specific heat $C_v<0$

$\frac{R}{\gamma -1}+\frac{R}{1-x}$ < 0

$\frac{1}{1.67-1}+\frac{1}{1-x}$ < 0

$\frac{1.67-x}{0.67(1-x)}$ <0

On further solving we get 1 < x < 1.67

The Correct Opt=D