Question #131855

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)?

Expert's answer

Let the molar specific heat of both system be same and equal to C.

If both system come to equilibrium at temperature T.

By conservation of energy,

Heat gained by first system= Heat loss by second system

N_{1}C_{1}(T-T_{1})=N_{2}C_{2}(T_{2}-T)

C1=C2=C

N_{1}C_{1}(T-T_{1})=N_{2}C_{2}(T_{2}-T)

C1=C2=C

N_{1}T-N_{1}T_{1}=N_{2}T_{2}-N_{2}T

T(N_{1}+N_{2})=T_{1}N_{1}+T_{2}N_{2}

T=(T_{1}N_{1}+T_{2}N_{2})/(N1+N2)=315.625K

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