Two thermodynamic processes are shown in the | vedclass

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

Question

(C) The equation of a polytropic process is $PV^x = 	ext{constant}$,which can be written as $\log P + x \log V = 	ext{constant}$,or $\log P = -x \lo

Vedclass · Accepted Answer

$C_P > C_B > C_A > C_V$

Vedclass · Answer

(C) The equation of a polytropic process is $PV^x = 	ext{constant}$,which can be written as $\log P + x \log V = 	ext{constant}$,or $\log P = -x \log V + 	ext{constant}$.Comparing this with the equation of a line $y = mx + c$,the slope $m = -x$.For process $A$,the slope is $	an(	heta_A) = \gamma$. Thus,$-x_A = \gamma$,so $x_A = -\gamma$.The molar heat capacity for a polytropic process is $C = C_V + \frac{R}{1-x}$.For process $A$,$C_A = C_V + \frac{R}{1 - (-\gamma)} = C_V + \frac{R}{1+\gamma}$. Since $\gamma > 1$,$C_A$ is a finite positive value.For process $B$,the slope is $	an(45^\circ) = 1$. Thus,$-x_B = 1$,so $x_B = -1$.For process $B$,$C_B = C_V + \frac{R}{1 - (-1)} = C_V + \frac{R}{2}$.Comparing the values:$C_P = C_V + R$$C_B = C_V + 0.5R$$C_A = C_V + \frac{R}{1+\gamma}$ (where $1 Thus,$C_P > C_B > C_A > C_V$.

Two thermodynamic processes are shown in the figure. The molar heat capacities for processes $A$ and $B$ are $C_A$ and $C_B$. The molar heat capacities at constant pressure and constant volume are represented by $C_P$ and $C_V$,respectively. Choose the correct statement.

Similar Questions

$2$ moles of a diatomic gas undergoes the process: $PT^2/V = \text{constant}$. The molar heat capacity of the gas during the process is:

Work done to increase the temperature of one mole of an ideal gas by $30^{\circ} C$, if it is expanding under the condition $V \propto T^{2/3}$ is, $(R = 8.314 \ J/mol \cdot K)$ (in $J$)

$A$ gas is found to obey the law $P^2V =$ constant. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume $3V_0$,its final temperature becomes

One mole of a monoatomic ideal gas is expanded by a process described by $p V^3 = C$,where $C$ is a constant. The heat capacity of the gas during the process is given by ($R$ is the gas constant).

$A$ monoatomic gas is taken through a process $TP^{-1/3} = \text{constant}$. If heat is given to the gas, what happens to its temperature?

Vedclass Test Series

Exam Paper Generator

Online Exam Module