Select the incorrect relation. (Where symbols | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) For an ideal gas,the change in internal energy is given by $\Delta U = n C_V \Delta T$.Using $C_V = \frac{R}{\gamma - 1}$,we get $\Delta U = n \le

Vedclass · Accepted Answer

$\Delta U = \frac{P_f V_f - P_i V_i}{1 - \gamma}$

Vedclass · Answer

(C) For an ideal gas,the change in internal energy is given by $\Delta U = n C_V \Delta T$.Using $C_V = \frac{R}{\gamma - 1}$,we get $\Delta U = n \left( \frac{R}{\gamma - 1} \right) (T_f - T_i)$.Since $PV = nRT$,we have $nRT_f = P_f V_f$ and $nRT_i = P_i V_i$.Substituting these,$\Delta U = \frac{P_f V_f - P_i V_i}{\gamma - 1}$.Comparing this with option $C$,we see that $\frac{P_f V_f - P_i V_i}{1 - \gamma} = - \left( \frac{P_f V_f - P_i V_i}{\gamma - 1} \right)$,which is incorrect. Thus,option $C$ is the incorrect relation.

	Gases		$C_P/C_V$ value
$A$	Monoatomic	$I$	$(4+f)/(3+f)$
$B$	Diatomic (rigid)	$II$	$5/3$
$C$	Diatomic (non-rigid)	$III$	$7/5$
$D$	Polyatomic	$IV$	$9/7$

Select the incorrect relation. (Where symbols have their usual meanings)

Similar Questions

What is the ratio of specific heats at constant pressure and constant volume for $NH_3$?

Using the law of equipartition of energy, the specific heat (in $J\, kg^{-1}\, K^{-1}$) of aluminium at room temperature can be estimated to be (atomic weight of aluminium $= 27$).

The amount of heat needed to raise the temperature of $4 \, \text{moles}$ of a rigid diatomic gas from $0^{\circ} \text{C}$ to $50^{\circ} \text{C}$ when no work is done is ......$R$ ($R$ is the universal gas constant).

Match the following ( $f$ is number of degrees of freedom):

Gases $C_P/C_V$ value

$A$ Monoatomic $I$ $(4+f)/(3+f)$

$B$ Diatomic (rigid) $II$ $5/3$

$C$ Diatomic (non-rigid) $III$ $7/5$

$D$ Polyatomic $IV$ $9/7$

The following sets of values for ${C_V}$ and ${C_P}$ of a gas have been reported by different students. The units are $cal/gm-mole-K$. Which of these sets is most reliable?

Vedclass Test Series

Exam Paper Generator

Online Exam Module