One mole of an ideal monatomic gas undergoes a process described by the equation textP textV3= 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 textP textV3= constant. The heat capacity of the gas during this process is (A) (3/2)R (B) (5/2)R (C) 2R (D) R

Tardigrade Admin · Accepted Answer

textP textV3= constant polytropic process with textn = 3 textC= textC textv+( textR/1 - textn) For monoatomic gas: textC textv=(3 textR/2) textC=(3 textR/2)+( textR/1 - 3) =(3 textR/2)-( textR/2) =(2 textR/2) textC= textR

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

$\frac{3}{2} R$

$\frac{5}{2} R$

$2 R$

$R$

$P V^{3} =$ constant polytropic process with $n = 3$
$C = C_{v} + \frac{R}{1 - n}$
For monoatomic gas : $C_{v} = \frac{3 R}{2}$
$C = \frac{3 R}{2} + \frac{R}{1 - 3}$
$= \frac{3 R}{2} - \frac{R}{2}$
$= \frac{2 R}{2}$
$C = R$

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= constant polytropic process with n=3 C=Cv​+1−nR​ For monoatomic gas : Cv​=23R​ C=23R​+1−3R​ =23R​−2R​ =22R​ C=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

$\frac{3}{2} R$

$\frac{5}{2} R$

$2 R$

$R$

$P V^{3} =$ constant polytropic process with $n = 3$
$C = C_{v} + \frac{R}{1 - n}$
For monoatomic gas : $C_{v} = \frac{3 R}{2}$
$C = \frac{3 R}{2} + \frac{R}{1 - 3}$
$= \frac{3 R}{2} - \frac{R}{2}$
$= \frac{2 R}{2}$
$C = R$