In a thermally isolated system,two boxes fill | vedclass

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

Question

(B) For a thermally isolated system,the total internal energy remains constant because $\Delta Q = 0$ and $\Delta W = 0$. Since the initial temperatur

Vedclass · Accepted Answer

$0.6$

Vedclass · Answer

(B) For a thermally isolated system,the total internal energy remains constant because $\Delta Q = 0$ and $\Delta W = 0$. Since the initial temperatures of both boxes are the same $(T)$,the final equilibrium temperature $T_f$ will also be $T$. Using the ideal gas law $PV = nRT$,we can find the number of moles in each box: $n_1 = \frac{P_1 V_1}{RT} = \frac{1 	imes V}{RT} = \frac{V}{RT}$ $n_2 = \frac{P_2 V_2}{RT} = \frac{0.5 	imes 4V}{RT} = \frac{2V}{RT}$ When the valve is opened,the total number of moles $n_{total} = n_1 + n_2$ occupies the total volume $V_{total} = V_1 + V_2 = V + 4V = 5V$ at temperature $T$. $n_{total} = \frac{V}{RT} + \frac{2V}{RT} = \frac{3V}{RT}$ Using the ideal gas law for the final state: $P_f V_{total} = n_{total} R T$ $P_f (5V) = \left(\frac{3V}{RT}ight) RT$ $P_f (5V) = 3V$ $P_f = \frac{3}{5} \, atm = 0.6 \, atm$.

Similar Questions

When one mole of monatomic gas is mixed with one mole of a diatomic gas,then the equivalent value of $\gamma$ for the mixture will be (vibration mode neglected).

$A$ vessel of volume $20 \ L$ contains a mixture of hydrogen and helium at a temperature of $27^{\circ} C$ and pressure $2 \ atm$. The mass of the mixture is $5 \ g$. Assuming the gases to be ideal,the ratio of the mass of hydrogen to that of helium in the given mixture will be:

$A$ gas mixture consists of $3$ moles of oxygen and $5$ moles of argon at temperature $T$. Assuming the gases to be ideal and the oxygen bond to be rigid,the total internal energy (in units of $RT$) of the mixture is

One mole of an ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of a diatomic gas $(\gamma = 7/5).$ What is $\gamma$ for the mixture? $\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

The ratio of specific heat of a mixture of one mole of helium and one mole of hydrogen gas will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module