Answer:
The value of final temperature of the mixture [tex]T_{3}[/tex] = 57.42 °c
Explanation:
Mass of first sample [tex]m_{1}[/tex] = 40.5 gram
Mass of second sample [tex]m_{2}[/tex] = 36.8 gram
Temperature of first sample [tex]T_{1}[/tex] = 85.7 °c
Temperature of second sample [tex]T_{2}[/tex] = 26.3 °c
The energy balance equation for the mixture is written as
[tex]m_{1}[/tex] [tex]T_{1}[/tex] + [tex]m_{2}[/tex] [tex]T_{2}[/tex] = [tex]m_{3}[/tex] [tex]T_{3}[/tex] ---------- ( 1 )
Total mass [tex]m_{3}[/tex] = [tex]m_{1}[/tex] + [tex]m_{2}[/tex]
Put the values of [tex]m_{1}[/tex] & [tex]m_{2}[/tex] in this equation we get,
⇒ [tex]m_{3}[/tex] = 40.5 + 36.8
⇒ [tex]m_{3}[/tex] = 77.3 gram -------- (2)
Put all the values of mass & temperature in equation 1 we get,
⇒ 40.5 × 85.7 + 36.8 × 26.3 = 77.3 × [tex]T_{3}[/tex]
⇒ 4438.69 = 77.3 × [tex]T_{3}[/tex]
⇒ [tex]T_{3}[/tex] = 57.42 °c
This is the value of final temperature of the mixture.
