An ideal gas is expanding such that PT^2 = te | vedclass

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

Question

(C) The coefficient of volume expansion is defined as $\gamma = \frac{1}{V} \left( \frac{dV}{dT} ight)$.Given the process equation: $PT^2 = 	ext{co

Vedclass · Accepted Answer

$\frac{3}{T}$

Vedclass · Answer

(C) The coefficient of volume expansion is defined as $\gamma = \frac{1}{V} \left( \frac{dV}{dT} ight)$.Given the process equation: $PT^2 = 	ext{constant}$.Using the ideal gas law $PV = nRT$, we can write $P = \frac{nRT}{V}$.Substituting $P$ into the process equation: $\left( \frac{nRT}{V} ight) T^2 = 	ext{constant}$.This simplifies to $\frac{T^3}{V} = 	ext{constant}$, or $V = k T^3$ (where $k$ is a constant).Differentiating $V$ with respect to $T$: $\frac{dV}{dT} = 3k T^2$.Now, substitute these into the expression for $\gamma$:$\gamma = \frac{1}{V} \left( \frac{dV}{dT} ight) = \frac{1}{kT^3} (3kT^2) = \frac{3}{T}$.

An ideal gas is expanding such that $PT^2 = \text{constant}$. The coefficient of volume expansion of the gas is

Similar Questions

Which of the following graphs represents the behavior of an ideal gas? Symbols have their usual meaning.

When the temperature of a gas at constant volume is increased by $5^{\circ}C$,its pressure increases by $0.5\%$ of its initial value. The initial temperature of the gas is..... $K$.

The $P-T$ diagram of an ideal gas having three different densities $\rho_1, \rho_2, \rho_3$ (in three different cases) is shown in the figure. Which of the following is correct?

Two vessels $A$ and $B$ are of the same size and are at the same temperature. Vessel $A$ contains $1 \ g$ of hydrogen and vessel $B$ contains $1 \ g$ of oxygen. If $P_{A}$ and $P_{B}$ are the pressures of the gases in $A$ and $B$ respectively,then the ratio $\frac{P_{A}}{P_{B}}$ is:

The volume of a given mass of a gas at $27^{\circ} C$ and $1$ $atm$ is $100$ $cc$. What will be its volume at $327^{\circ} C$ if the pressure remains constant (in $cc$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module