One mole of an ideal monatomic gas undergoes a process described by the equation PV3= constant. The heat capacity of the gas during this process is -

Question

One mole of an ideal monatomic gas undergoes a process described by the equation PV3= constant. The heat capacity of the gas during this process is - (A) (3/2)R (B) (5/2)R (C) 2 R (D) R

Tardigrade Admin · Accepted Answer

PV3 =C (n=3) Specific heat in polytropic process PVn =K C =CV + (R/1-n) = (3/2) R + (R/1-3) = (3/2) R - (R/2) = R

Q. One mole of an ideal monatomic gas undergoes a process described by the equation $P V^{3} =$ constant. The heat capacity of the gas during this process is -

$\frac{3}{2} R$

$\frac{5}{2} R$

$2 R$

$R$

$P V^{3} = C (n = 3)$
Specific heat in polytropic process
$P V^{n} = K$
$C = C_{V} + \frac{R}{1 - n}$
$= \frac{3}{2} R + \frac{R}{1 - 3}$
$= \frac{3}{2} R - \frac{R}{2} = R$

Q. One mole of an ideal monatomic gas undergoes a process described by the equation PV3= constant. The heat capacity of the gas during this process is -

23​R

25​R

2R

R

PV3=C(n=3) Specific heat in polytropic process PVn=K C=CV​+1−nR​ =23​R+1−3R​ =23​R−2R​=R

Q. One mole of an ideal monatomic gas undergoes a process described by the equation $P V^{3} =$ constant. The heat capacity of the gas during this process is -

$\frac{3}{2} R$

$\frac{5}{2} R$

$2 R$

$R$

$P V^{3} = C (n = 3)$
Specific heat in polytropic process
$P V^{n} = K$
$C = C_{V} + \frac{R}{1 - n}$
$= \frac{3}{2} R + \frac{R}{1 - 3}$
$= \frac{3}{2} R - \frac{R}{2} = R$