Question

Three liquids are at temperatures of 6 ◦C, 23◦C, and 38◦C, respectively. Equal masses of the first two liquids are mixed, and the equilibrium temperature is 13◦C. Equal masses of the second and third are then mixed, and the equilibrium temperature is 26.8 ◦C. Find the equilibrium temperature.

Answer 1

The equilibrium temperature is T13=3.12 ◦C

Explanation:

Given

The temperature of liquids: T1=6◦C, T2=23◦C, T3=38◦C

The temperature of 1+2 liquids mix: T12= 13◦C.

The temperature of 2+3 liquids mix: T23=26.8 ◦C.

The temperature of 1+3 liquids mix: T13= ??

1.When the first two liquids are mixed:

• mC1(T1-T12)+mC2(T2-T12)=0
• C1(6-13)=C2(23-13)=0
• 7C1=10C2
• C1=1.42C2

2.When the second and third liquids are mixed:

• mC2(T2-T23)+mC3(T3-T23)=0
• C2(23-26.8)=C3(38-26.8)=0
• 3.8C2=12.8C3
• C2=3.36C3

3.When the first and third liquids are mixed:

• mC1(T1-T13)+mC3(T3-T13)=0
• C1(6-T13)+C3(38-T13)=0
• C1=1.42C2  C2=3.36C3
• C1=1.42C2(3.36C3)
• C1=4.77C3
• C1(6-T13)+C3(38-T13)=0
• 4.77C3(6-T13)+C3(38-T13)=0
• By solving the equation we get,
• T13=3.12 ◦C
• The equilibrium temperature is T13=3.12 ◦C