A monatomic ideal gas undergoes a process in which the ratio of P to V at any instant is constant and equals to 1 . What is the molar heat capacity of the gas?

Question

A monatomic ideal gas undergoes a process in which the ratio of P to V at any instant is constant and equals to 1 . What is the molar heat capacity of the gas? (A) (4 R/2) (B) (3 R/2) (C) (5 R/2) (D) 0

Tardigrade Admin · Accepted Answer

A monoatomic ideal gas undergoes a process in which the ratio of

P

to

V

at any instant is constant and equals

1

.

\frac{P}{V} =

constat

P V^{- 1} =

constant

P V^{γ} =

constant

γ = - 1

Monoatomic gas:

C_{V} = \frac{3}{2} R

Molar heat capacity

= C_{V} + \frac{R}{1 - γ}

= \frac{3}{2} R + \frac{R}{1 - ( - 1 )}

= \frac{3}{2} R + \frac{R}{2} = \frac{4 R}{2}

Q. A monatomic ideal gas undergoes a process in which the ratio of $P$ to $V$ at any instant is constant and equals to $1$ . What is the molar heat capacity of the gas?

$\frac{4 R}{2}$

$\frac{3 R}{2}$

$\frac{5 R}{2}$

$0$

Q. A monatomic ideal gas undergoes a process in which the ratio of P to V at any instant is constant and equals to 1 . What is the molar heat capacity of the gas?

24R​

23R​

25R​

0

A monoatomic ideal gas undergoes a process in which the ratio of P to V at any instant is constant and equals 1 . VP​= constat PV−1= constant PVγ= constant γ=−1 Monoatomic gas: CV​=23​R Molar heat capacity =CV​+1−γR​ =23​R+1−(−1)R​ =23​R+2R​=24R​

Q. A monatomic ideal gas undergoes a process in which the ratio of $P$ to $V$ at any instant is constant and equals to $1$ . What is the molar heat capacity of the gas?

$\frac{4 R}{2}$

$\frac{3 R}{2}$

$\frac{5 R}{2}$

$0$