An ideal gas expands in such a way that PV^2 | vedclass

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

Question

(D) Given the process equation: $PV^2 = 	ext{constant}$.Using the ideal gas law $PV = nRT$, we can write $P = \frac{nRT}{V}$.Substituting this into t

Vedclass · Accepted Answer

Such an expansion is possible only with cooling.

Vedclass · Answer

(D) Given the process equation: $PV^2 = 	ext{constant}$.Using the ideal gas law $PV = nRT$, we can write $P = \frac{nRT}{V}$.Substituting this into the process equation: $\left(\frac{nRT}{V}ight) V^2 = 	ext{constant}$.This simplifies to $nRT \cdot V = 	ext{constant}$.Since $n$ and $R$ are constants, we get $TV = 	ext{constant}$, or $T \propto \frac{1}{V}$.The graph of $T$ versus $V$ is a rectangular hyperbola, not a parabola or a straight line.For an expansion, $V$ increases. Since $T \propto \frac{1}{V}$, as $V$ increases, $T$ must decrease.Therefore, such an expansion is possible only with cooling.

An ideal gas expands in such a way that $PV^2 =$ constant throughout the process.

Similar Questions

Hydrogen gas is undergoing a process given by $PV^2 = \text{constant}$. The ratio of work done by the gas to the change in its internal energy is

The pressure and volume of an ideal gas are related as $PV^{3/2} = K$ (constant). The work done when the gas is taken from state $A(P_1, V_1, T_1)$ to state $B(P_2, V_2, T_2)$ is:

An ideal gas is subjected to a thermodynamic process $PV^{2.5} = 0.40$,where $P$ is in $Pa$ and $V$ is in $m^3$. What is the slope of the $P-V$ curve with volume plotted against the $x-$axis at $V = 1 \, m^3$?

$1 \, \text{mole}$ of an ideal gas at temperature $T_1$ expands according to the law $P/V = \text{constant}$. Find the work done when the final temperature becomes $T_2$.

$P_i, V_i$ and $P_f, V_f$ are initial and final pressures and volumes of a gas in a thermodynamic process respectively. If $PV^n = \text{constant}$, then the amount of work done is

Vedclass Test Series

Exam Paper Generator

Online Exam Module