Question

pls solve this question. no spam. correct answer only.​

Answer 1

Question :

A monoatomic ideal gas is following the cyclic process ABCA. Then choose the correct option.

Solution :

For path AB

$\sf:\implies\:TV=constant$

$\sf:\implies\:PV^2=constant\:\dots\:(I)$

For polytropic process

• $\sf{PV^m=constant}\:\dots\:(II)$

On comparing eqn. (I) and (II)

$\bf:\implies\:m=2$

The molar heat capacity is given as

$\sf:\implies\:C=\dfrac{R}{\gamma-1}-\dfrac{R}{m-1}$

For monoatomic gas, $\sf\gamma=\dfrac{5}{3}$

$\sf:\implies\:C=\dfrac{3R}{2}-R=\dfrac{R}{2}$

$\sf:\implies\:C=\dfrac{R}{\left(\dfrac{5}{3}-1\right)}-\dfrac{R}{2-1}$

$\sf:\implies\:C=\dfrac{3R}{2}-R$

$:\implies\:\underline{\boxed{\bf{\orange{C=\dfrac{R}{2}}}}}$

∴ Option (a) is correct!

For BC it is an isochoric process and temperature is decreasing so option (b) is correct.

$\sf:\implies\:C=C_v=\dfrac{3R}{2}$

;so option (c) is wrong.

For process CA (isothermal)

$\sf:\implies\:W=nRT\ln\left(\dfrac{V_A}{V_C}\right)$

$\sf:\implies\:W=\dfrac{2}{3}\left(\dfrac{3}{2}nRT\right)\ln(4)$

As density at C is 4ρ｡

$:\implies\:\underline{\boxed{\bf{\gray{W=\dfrac{2}{3}U_o\ln(4)}}}}$

So, option (d) is correct.