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# Answer to Question #127007 in Mechanical Engineering for Zakir Hussain

Question #127007
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
2020-07-27T07:23:39-0400

we know that, for two particular system we have,"T_1=175 K,T_2=400K"

"n_1=3,n_2=5,"

we know that

"\\frac{1}{T}=\\frac{3}{2}R (\\frac{n}{U})"

for two different temperature

"\\frac{1}{T_1}=\\frac{3}{2}R (\\frac{n_1}{U_1})"

"\\frac{1}{175}=\\frac{3}{2}R (\\frac{3}{U_1})"

"U_1=6547.275"

similarly for other system

"\\frac{1}{T_2}=\\frac{3}{2}R (\\frac{n_2}{U_2})"

"\\frac{1}{400}=\\frac{3}{2}R (\\frac{5}{U_2})"

"U_2=24942 J"

so,

"U=U_2-U_1=24942-6547.275"

so, during equilibrium condition

"\\frac{1}{T}=\\frac{3}{2}R (\\frac{n}{U})"

"\\frac{1}{T}=\\frac{3}{2}(8.314)(\\frac{8}{18394.725})"

T= 184.375 K

This is the equilibrium temperature

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