Home
Class 11
PHYSICS
Two thermally insulated vessel 1 and 2 a...

Two thermally insulated vessel 1 and 2 are filled with air at temperature `(T_1T_2), volume (V_1V_2)` and pressure `(P_1P_2)` respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

A

`T_1+T_2`

B

`(T_1+T_2)//2`

C

`(T_1T_2(P_1V_1+P_2V_2))/(P_1V_1T_2+P_2V_2T_1)`

D

`(T_1T_2(P_1V_1+P_2V_2))/(P_1V_1T_1+P_2V_2T_2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Since, number of moles of the system remains same
`(P_1V_1)/(RT_1)+(P_2V_2)/(RT_2)=(P(V_1+V_2))/(RT)`
`implies T=(P(V_1+V_2)T_1T_2)/((P_1V_1T_2+P_2V_2T_1))`
According to Boyle.s law,
`P_1V_1+P_2V_2=P(V_1+V_2)`
`T=((P_1V_1+P_2V_2)T_1T_2)/((P_1V_1T_2+P_2V_2T_1))`
Promotional Banner

Similar Questions

Explore conceptually related problems

Two thermally insulated vessels are filled with an ideal gas. The pressure, volume and temperature in the two vessels are P_(1), V_(1), T_(1) and P_(2), V_(2), T_(2) respectively. Now, the two vessels are connected using a short insulating tube. (a) Find final temperature of the gas. (b) Express the final pressure of the gas in terms of P_(1), V_(1), P_(2) and V_(2) only.

Two thermally insulated vessels 1 and 2 are filled with air and connected by a short tube equipped with a valve. The volumes of the vessels, the pressures and temperature of air in them are know (V_1,p_1,T_1 and V_2,p_2,T_2 ). Find the air temperature and pressure established after the opening of the valve.

Two identical vessels contain the same gas at pressure P_(1) and P_(2) at absolute temperature T_(1) and T_(2) , respectively. On joining the vessels with a small tube as shown in the figure. The gas reaches a common temperature T and a common pressure P. Determine the ratio P//T

Two containers of equal volume contain the same gas at pressure P_(1) and P_(2) and absolute temperature T_(1) and T_(2) , respectively. On joining the vessels, the gas reaches a common pressure P and common temperature T . The ratio P//T is equal to