C P and C V are specific heats at constant pressure and constant volume respectively. It is observed that C P - C V = a for helium gas C P - C V = b for oxygen gas Such that, b is n times the a. Find out value of n.

Question

C P and C V are specific heats at constant pressure and constant volume respectively. It is observed that C P - C V = a for helium gas C P - C V = b for oxygen gas Such that, b is n times the a. Find out value of n. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Let molar heat capacity at constant pressure

= SP

and molar heat capacity at constant volume

= s_{V}

∴ S_{P} - S_{V} = R

Now, principal specific heat,

C = \frac{s}{M}

∴ C_{P} - C_{V} = \frac{R}{M}

∴

For

He, a = \frac{R}{4};

for

O_{2}, b = \frac{R}{32}

∴ \frac{b}{a} = \frac{R}{32} \times \frac{4}{R} = \frac{1}{8}

\Rightarrow b = 0.125 a = 0.13 a

...(Rounding off to two digits)

Q. CP​ and CV​ are specific heats at constant pressure and constant volume respectively. It is observed that CP​−CV​=a for helium gas CP​−CV​=b for oxygen gas Such that, b is n times the a. Find out value of n.

Let molar heat capacity at constant pressure =SP and molar heat capacity at constant volume =sV​ ∴SP​−SV​=R Now, principal specific heat, C=Ms​ ∴CP​−CV​=MR​ ∴ For He,a=4R​; for O2​,b=32R​ ∴ab​=32R​×R4​=81​ ⇒b=0.125a=0.13a ...(Rounding off to two digits)

Q. $C_{P}$ and $C_{V}$ are specific heats at constant pressure and constant volume respectively. It is observed that
$C_{P} - C_{V} = a$ for helium gas
$C_{P} - C_{V} = b$ for oxygen gas
Such that, $b$ is $n$ times the $a$ . Find out value of $n$ .