In an adiabatic change,the pressure and tempe | vedclass

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

Question

(C) For an adiabatic process,the relation between pressure $p$ and volume $V$ is given by Poisson's equation: $p V^{\gamma} = 	ext{constant}$.Using t

Vedclass · Accepted Answer

$\frac{5}{2}$

Vedclass · Answer

(C) For an adiabatic process,the relation between pressure $p$ and volume $V$ is given by Poisson's equation: $p V^{\gamma} = 	ext{constant}$.Using the ideal gas law $pV = RT$,we can write $V = \frac{RT}{p}$.Substituting this into the adiabatic equation:$p \left( \frac{RT}{p} ight)^{\gamma} = 	ext{constant}$$p^{1-\gamma} T^{\gamma} = 	ext{constant}$$p \propto T^{\frac{\gamma}{\gamma-1}}$.Comparing this with the given relation $p \propto T^{C}$,we get $C = \frac{\gamma}{\gamma-1}$.For a monoatomic gas,the adiabatic index $\gamma = \frac{5}{3}$.Substituting the value of $\gamma$:$C = \frac{5/3}{5/3 - 1} = \frac{5/3}{2/3} = \frac{5}{2}$.

In an adiabatic change,the pressure and temperature of a monoatomic gas are related by the relation $p \propto T^{C}$,where $C$ is equal to

Similar Questions

An ideal gas is found to obey $p V^{3/2} = \text{constant}$ during an adiabatic process. If such a gas initially at a temperature $T$ is adiabatically compressed to half of its initial volume, then its final temperature is

Initial pressure and volume of a monoatomic ideal gas are $P$ and $V$. The change in internal energy of this gas in adiabatic expansion to volume $V_{final} = 27V$ is . . . . . . $J$.

The $P-V$ diagram for two gases during an adiabatic process is shown in the figure. Curves $A$ and $B$ correspond to:

If the pressure in an adiabatic process increases by $\frac{2}{3}\%$,then the percentage decrease in volume will be ....... . Assume $C_P/C_V = 3/2$.

$5.6\, L$ of helium gas at $STP$ is adiabatically compressed to $0.7\, L$. Taking the initial temperature to be $T_1$,the magnitude of work done in the process is

Vedclass Test Series

Exam Paper Generator

Online Exam Module