One mole of hydrogen gas at temperature T is mixed with one mole of helium gas at temperature 2 T in an isolated vessel. The equilibrium temperature of the gas mixture is

Question

One mole of hydrogen gas at temperature T is mixed with one mole of helium gas at temperature 2 T in an isolated vessel. The equilibrium temperature of the gas mixture is (A) (11/8) barT (B) (5/4) T (C) (3/2) T (D) (7/5) T

Tardigrade Admin · Accepted Answer

Equating internal energy (5/2) R T × 1+(3/2) × 1 × R(2 T)=Ui Uf=(5/2) R T'+(3/2) R T'=4 R T' [final internal energy] ∴ (11 R T/2)=4 R T' ∴ T'=(11/8) T

Q. One mole of hydrogen gas at temperature $T$ is mixed with one mole of helium gas at temperature $2 T$ in an isolated vessel. The equilibrium temperature of the gas mixture is

$\frac{11}{8} \overset{ˉ}{T}$

$\frac{5}{4} T$

$\frac{3}{2} T$

$\frac{7}{5} T$

Equating internal energy
$\frac{5}{2} RT \times 1 + \frac{3}{2} \times 1 \times R (2 T) = U_{i}$
$U_{f} = \frac{5}{2} R T^{'} + \frac{3}{2} R T^{'} = 4 R T^{'}$ [final internal energy]
$∴ \frac{11 RT}{2} = 4 R T^{'}$
$∴ T^{'} = \frac{11}{8} T$

Q. One mole of hydrogen gas at temperature T is mixed with one mole of helium gas at temperature 2T in an isolated vessel. The equilibrium temperature of the gas mixture is

811​Tˉ

45​T

23​T

57​T