Question
n1 moles of gas A at temperature T1 and n2 moles of gas B at temperature T2 are mixed together without loss of energy. Find the temperature of mixture.
Solution
Gas A:
Number of moles of gas = n1
Temperature = T1
K.E of 1 molecule of gas =
Total K.E =
Gas B:
Number of moles of gas = n2
Temperature = T2
K.E of 1molecue =
Total K.E = n2 N
Now, total kinetic energy of the mixture is,
... (1)
Let, the temperature of the mixture at equilibrium be T. The total K.E of the mixture at equilibrium is given by,
K.E = ...(2)
Now, using equations (1) and (2), we have
Number of moles of gas = n1
Temperature = T1
K.E of 1 molecule of gas =
Total K.E =
Gas B:
Number of moles of gas = n2
Temperature = T2
K.E of 1molecue =
Total K.E = n2 N
Now, total kinetic energy of the mixture is,
... (1)
Let, the temperature of the mixture at equilibrium be T. The total K.E of the mixture at equilibrium is given by,
K.E = ...(2)
Now, using equations (1) and (2), we have
