Answer to Question #131855 in Mechanical Engineering for Mona

Question

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)?

Answer 1

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

N₁C₁(T-T₁)=N₂C₂(T₂-T)

C1=C2=C

N₁C₁(T-T₁)=N₂C₂(T₂-T)

C1=C2=C

N₁T-N₁T₁=N₂T₂-N₂T

T(N₁+N₂)=T₁N₁+T₂N₂

T=(T₁N₁+T₂N₂)/(N1+N2)=315.625K