Question

Two systems have the following equations of state and are contained in a closed cylinder, separated by a fixed, adiabatic and impermeable piston. N1=2, N2=1.5

. The initial temperatures are T1 = 175 K and T2 = 400 K. The total volume is 0.025 m^3

. The piston is allowed to move and heat transfer is allowed across the piston. Determine the final temperature of the system (in Kelvin).

1/T1=3/2(R*N1/U1) , P1/T1=R*N1/V1

1/T2=5/2(R*N2/U2) , P2/T2=R*N2/V2

Answer 1

Let $V_1 ,V_2$ are the volume of two system

Now,

$V_1+V_2= V= 0.025 m^3$

As both system are in closed container in adiabatic condition

$T_1=175 K,T_2=400 K$

we know that, PV=nRT

$\frac{nRT_1}{P_1}+\frac{nRT_2}{P_2}= \frac{nRT}{P}$

$\frac{2R\times 175}{P}+\frac{1.5R\times 400}{P}= \frac{3.5RT}{P}$

T= 270.42 K, This is the final temeprature