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NEET PHYSICSMedium

One mole of an ideal monatomic gas undergoes a process described by the equation PV3=constantPV^3 = \text{constant}. The heat capacity of the gas during this process is:

A

32R\frac{3}{2}R

B

52R\frac{5}{2}R

C

2R2R

D

RR

Step-by-Step Solution

The process described is a polytropic process of the form PVn=constantPV^n = \text{constant}, where the polytropic index n=3n = 3.

The molar heat capacity (CC) of an ideal gas in a polytropic process is given by the formula: C=CV+R1−nC = C_V + \frac{R}{1-n}

For a monatomic ideal gas, the molar heat capacity at constant volume is: CV=32RC_V = \frac{3}{2}R

Substituting the values into the formula: C=32R+R1−3C = \frac{3}{2}R + \frac{R}{1-3} C=32R+R−2C = \frac{3}{2}R + \frac{R}{-2} C=32R−12RC = \frac{3}{2}R - \frac{1}{2}R C=22R=RC = \frac{2}{2}R = R

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