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

Question

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

Tardigrade Admin · Accepted Answer

As there is no loss of energy, Δ U1+Δ U2=0 n1 Cν(T-T1)+n2 Cν(T-T2)=0 CV= Specific heat at constant volume. ⇒ n1 T+n2 T=n1 T1+n2 T2 or T=((n1 T1+n2 T2/n1+n2)).

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

$T_{1} + T_{2}$

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

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

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

As there is no loss of energy,
$Δ U_{1} + Δ U_{2} = 0$
$n_{1} C_{ν} (T - T_{1}) + n_{2} C_{ν} (T - T_{2}) = 0$
$C_{V} =$ Specific heat at constant volume.
$\Rightarrow n_{1} T + n_{2} T = n_{1} T_{1} + n_{2} T_{2}$
or $T = (\frac{n _{1} T _{1} + n _{2} T _{2}}{n _{1} + n _{2}})$ .

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

T1​+T2​

2T1​+T2​​

n1​+n2​n1​T1​+n2​T2​​

n1​+n2​n1​T1​−n2​T2​​