Two perfect gases at absolute temperatures T1 and T2 are mixed. There is no loss of energy. The temperature of mixture of masses of molecules are m1 and m2 and the number of molecules in the gases are n1 and n2 respectively, is

Question

Two perfect gases at absolute temperatures T1 and T2 are mixed. There is no loss of energy. The temperature of mixture of masses of molecules are m1 and m2 and the number of molecules in the gases are n1 and n2 respectively, is (A)  ( T1 + T2 / 2 )  (B)  ( n1 T1 + n2T2 / n1 + n2 )  (C)  ( n1 T2 + n2T1 / n1 + n2 )  (D)  √ T1 T2 / n1n2

Tardigrade Admin · Accepted Answer

We know E = (3/ 2) n kT k =Boltzmann's constant ∴ (3/ 2) n1 k T1 + (3/ 2) n2 k T2 = (3/ 2) (n1 + n2) k T T = ( n1 T1 + n2T2 / n1 + n2 )

Q. Two perfect gases at absolute temperatures $T_{1}$ and $T_{2}$ are mixed. There is no loss of energy. The temperature of mixture of masses of molecules are $m_{1}$ and $m_{2}$ and the number of molecules in the gases are $n_{1}$ and $n_{2}$ respectively, is

$\frac{T _{1} + T _{2}}{2}$

$\frac{n _{1} T _{1} + n _{2} T _{2}}{n _{1} + n _{2}}$

$\frac{n _{1} T _{2} + n _{2} T _{1}}{n _{1} + n _{2}}$

$T_{1} T_{2} / n_{1} n_{2}$

We know E = $\frac{3}{2} nk T$
k =Boltzmann's constant
$∴ \frac{3}{2} n_{1} k T_{1} + \frac{3}{2} n_{2} k T_{2} = \frac{3}{2} (n_{1} + n_{2}) k T$
T = $\frac{n _{1} T _{1} + n _{2} T _{2}}{n _{1} + n _{2}}$

Q. Two perfect gases at absolute temperatures T1​ and T2​ are mixed. There is no loss of energy. The temperature of mixture of masses of molecules are m1​ and m2​ and the number of molecules in the gases are n1​ and n2​ respectively, is

2T1​+T2​​

n1​+n2​n1​T1​+n2​T2​​

n1​+n2​n1​T2​+n2​T1​​

T1​T2​/n1​n2​​