During an experiment, an ideal gas is found t | vedclass

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

Question

(B) Given the law for the ideal gas process: $VP^2 = K$ (where $K$ is a constant).From the ideal gas equation, we have $PV = nRT$, which implies $P =

Vedclass · Accepted Answer

$T' = \sqrt{2} T$

Vedclass · Answer

(B) Given the law for the ideal gas process: $VP^2 = K$ (where $K$ is a constant).From the ideal gas equation, we have $PV = nRT$, which implies $P = \frac{nRT}{V}$.Substituting this into the given law:$V \left( \frac{nRT}{V} \right)^2 = K$$V \left( \frac{n^2 R^2 T^2}{V^2} \right) = K$$\frac{n^2 R^2 T^2}{V} = K$Since $n$ and $R$ are constants, we can write $T^2 \propto V$, or $T \propto \sqrt{V}$.Therefore, $\frac{T_2}{T_1} = \sqrt{\frac{V_2}{V_1}}$.Given $V_1 = V$, $T_1 = T$, and $V_2 = 2V$, we have:$\frac{T'}{T} = \sqrt{\frac{2V}{V}} = \sqrt{2}$.Thus, $T' = \sqrt{2} T$.

During an experiment, an ideal gas is found to obey an additional law $VP^2 = \text{constant}$. The gas is initially at temperature $T$ and volume $V$. What will be the temperature of the gas when it expands to a volume $2V$?

Similar Questions

The figure shows the pressure $P$ versus volume $V$ graphs for two different gas samples at a given temperature. $M_A$ and $M_B$ are the masses of the two samples,and $n_A$ and $n_B$ are the numbers of moles. Which of the following must be incorrect?

Explain why the air pressure in a car tire increases while the car is in motion.

$A$ gas at $27^{\circ}C$ has a volume $V$ and pressure $P$. If it is heated such that the pressure becomes double and the volume becomes triple,what is the final temperature in $^{\circ}C$?

At constant temperature,increasing the pressure of a gas by $5 \%$ its volume will decrease by (in $\%$)

For a given mass of a gas at constant temperature, the volume and the pressure are $V$ and $P$ respectively. Then the slope of the graph drawn between $\log_e V$ on the $X$-axis and $\log_e P$ on the $Y$-axis is

Vedclass Test Series

Exam Paper Generator

Online Exam Module