Question

thermally insulated vessels 1 and 2 are filled with air at temperature T1 and t2 volume V1 V2 pressure P1 P2 respectively the value in the two vessels is opened the temperature inside the vessel at equilibrium will be

Answer 1

P1V1/T1=P2V2/T2...................

Answer 2

$<b>$No of moles of system remains same

$\dfrac{P_1V_1}{RT_1} + \dfrac{P_2V_2}{RT_2} = \dfrac{P(V_1 + V_2)}{RT}$

$T \: \: = \: \dfrac{P(V_1 + V_2)T_1T_2}{P_1V_1T_2 + P_2V_2T_1}$

According to Boyle's law

$P_1V_1 + P_2V_2 = P(V_1 + V_2)$

$T \: \: = \: \: \dfrac{(P_1V_1 + P_2V_2)T_1T_2}{(P_1V_1T_2 + P_2V_2T_1)}$