Question

One mole of an ideal monoatomic gas is taken along the process in which $P{V}^x=constant$. The graph shown represents the variation of molar heat capacity of such a gas which respect to ${}^{\prime }{x}^{\prime }$. The values of $c^{\prime }$ and $x^{\prime }$, respectively, are given by_____________.

• A. $\frac{5}{2}R,\frac{5}{2}$
• B. $\frac{5}{2}R,\frac{5}{3}$
• C. $\frac{7}{2}R,\frac{7}{2}$
• D. $\frac{5}{2}R,\frac{7}{5}$

Answer 1

Answer: (B)

$\frac{5}{2}R,\frac{5}{3}$

Given :

$p{v}^x=constant$

$e=C_v+\frac{R}{1-x}$

$C=\frac{3R}{2}+\frac{R}{1-x}$

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

$C_{20}=dfrac3-3x+22(1-x)R$

$C=\left(\frac{5-3x}{2(1-x)}\right)R$

for $C=0$

$x=x^1=\frac{5}{3}$

for $x=0$

$C=C^1=\frac{5R}{2}$

Option B is correct.