Question

a ideal monoatomic gas undergoes a process follow the relation P directly proportional to V the molar heat capacity of the gas is​

Answer 1

Answer:

Explanation:

PV^-1 =k

Compare it with PV^x=k

We will get x=-1

Answer 2

Answer: The molar heat capacity of the gas for the given process is 2R

Explanation:

A gaseous process of form PVⁿ = k, where k is a positive constant, is called a polytropic process.

P denotes pressure and V denotes volume of the ideal gas.

The specific molar heat capacity for such processes is given by the following formula :

$C_m = C_V + \frac{R}{1-n}$

$C_m$ ⇒ Molar heat capacity

$C_V$  ⇒ Heat capacity at constant volume

R  ⇒ Universal gas constant

Given :  P ∝ V

∴ P = KV

⇒ PV⁻¹  =  K

Comparing it with a polytropic process,

PV⁻¹  =  PVⁿ

⇒ n = -1

For monoatomic gas : $C_V = \frac{3R}{2}$

$C_m = C_V + \frac{R}{1-n}$

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

$C_m = \frac{3R}{2} + \frac{R}{2}$

$C_m = 2R$

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