Question 462: Thermodynamics & KTG

Question

Three perfect gases at absolute temperatures ${T_1},\,{T_2}$ and ${T_3}$ are mixed. The masses of molecules are ${m_1},{m_2}$ and ${m_3}$ and the number of molecules are ${n_1},$ ${n_2}$ and ${n_3}$ respectively. Assuming no loss of energy, the final temperature of the mixture is:

Accepted Answer

Number of moles of first gas $ = {{{n_1}} \over {{N_A}}}$
Number of moles of second gas $ = {{{n_2}} \over {{N_A}}}$
Number of moles of third gas $ = {{{n_3}} \over {{N_A}}}$
If there is no loss of energy then
${P_1}{V_1} + {P_2}{V_2} + {P_3}{V_3} = PV$
${{{n_1}} \over {{N_A}}}R{T_1} + {{{n_2}} \over {{N_A}}}R{T_2} + {{{n_3}} \over {{N_A}}}R{T_3}$
$ = {{{n_1} + {n_2} + {n_3}} \over {{N_A}}}R{T_{mix}}$
$ \Rightarrow {T_{mix}} = {{{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}} \over {{n_1} + {n_2} + {n_3}}}$

Answer

${{{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}} \over {{n_1} + {n_2} + {n_3}}}$

Answer

${{{n_1}T_1^2 + {n_2}T_2^2 + {n_3}T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}$

Answer

${{n_1^2T_1^2 + n_2^2T_2^2 + n_3^2T_3^2} \over {{n_1}{T_1} + {n_2}{T_2} + {n_3}{T_3}}}$

Answer

${{\left( {{T_1} + {T_2} + {T_3}} \right)} \over 3}$

Thermodynamics & KTG

Three perfect gases at absolute temperatures {T_1},\,{T_2} and {T_3} are mixed. The masses of molecules are {m_1},{m_2} and {m_3} and the number of molecules are {n_1}, {n_2} and {n_3} respectively. Assuming no loss of energy, the final temperature of the mixture is:

Choose the correct answer: