Question #131921

Two systems have the following equations of state, where R is the gas constant per mole. The mole numbers are N1 = 3 and N2 = 5. The initial temperatures are T1 = 175 K and T2 = 400 K. What is the temperature once equilibrium is reached (in Kelvin)?

1/T1=3/2×R×N1/U1

1/T2=5/2×R×N2/U2

Expert's answer

we know that

1/T=3/2R(n/U)

for two different temperature

1/T_{1}=3/2R(n_{1}/u_{1})

1/175=3/2 R(3/U_{1})

U_{1}=6547.275

similarity for other system

1/T_{2}=3/2R (N_{2}/U_{2})

1/400=3/2 R(5/U_{2})

U_{2 }=24942 J

so

U =U_{2}_u_{1}=24942 _6547.275

so during equilibrium condition

1/T=3/2R(n/U)

=3/2(8.314)(8/18394.725)

T = 184.375K

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