Question

A)   When 155 mL of water at 26 degrees Celsius is mixed with 25 mL of water at 85 degrees Celsius what is the final temperature? (Assume that no heat is released to the surroundings, d of water = 1.00 g/mL

B) Use twice the volume of each water sample. Calculate final temperature.

C) Instead of 75 mL, use 150 mL.  Calculate final temperature.

D) Instead of 75 mL, use 25 mL.  Calculate final temperature.

E) Discuss your results. How did the different volumes affect the final temperature?

Answer 1

Answer -

Density of water = 1g/mL

A)

Given

Volume of water at 26 C = 155 ml

Volume of water at 85 C = 25 ml

Final Temperature = ?

We know that,

Density = Mass /Volume

Mass = Density * Volume

So,

Mass of 155 ml of water = 155 ml * 1g/ml = 155 g

Mass of 25 ml of water = 25 ml * 1g/ml = 25 g

Now,

Heat = m*s* (T_final - T_initial)

where, s = specific heat

m = mass

So,

Heat lost = - heat gained

155 g * s * (T_final - 26 C) = - [25 g * s * (T_final - 85 C)]

155 g * T_final - 155 g * 26 C = 25 g * 85 C - 25 g *T_final

155 g * T_final + 25 g *T_final = 25 g * 85 C + 155 g * 26 C

T_final * 180 g = 2125 g C + 4030 g C

T_final * 180 g = 6155 g C

T_final  = 6155 g C / 180 g

T final = 34.19 C [ANSWER]

B) Twice Volume of each.

T final = ?

Volume of water at 26 C = 155 ml * 2 = 310 ml

Volume of water at 85 C = 25 ml * 2 = 50 ml

Final Temperature = ?

We know that,

Density = Mass /Volume

Mass = Density * Volume

So,

Mass of 310 ml of water = 155 ml * 1g/ml = 310 g

Mass of 50 ml of water = 50 ml * 1g/ml = 50 g

Now,

Heat = m*s* (T_final - T_initial)

where, s = specific heat

m = mass

So,

Heat Lost = - Heat Gained

310 g * s * (T_final - 26 C) = - [50 g * s * (T_final - 85 C)]

310 g * T_final - 310 g * 26 C = 50 g * 85 C- 50 g *T_final

310 g * T_final + 50 g *T_final = 50 g * 85 C + 310 g * 26 C

T_final * 360 g = 4250 g C + 8060 g C

T_final * 360 g = 12310 g C

T_final  = 12310 g C / 360 g

T final = 34.19 C [ANSWER]

C)

There is no 75 ml in the question but i am assuming that you are asking to make 25 ml to 150 ml.

Volume of water at 26 C = 155 ml

Volume of water at 85 C = 150 ml

Final Temperature = ?

We know that,

Density = Mass /Volume

Mass = Density * Volume

So,

Mass of 155 ml of water = 155 ml * 1g/ml = 155 g

Mass of 150 ml of water = 150 ml * 1g/ml = 150 g

Now,

Heat = m*s* (T_final - T_initial)

where, s = specific heat

m = mass

So,

Heat lost = - Heat Gained

155 g * s * (T_final - 26 C) = - [150 g * s * (T_final - 85 C)]

155 g * T_final - 155 g * 26 C = 150 g * 85 C - 150 g *T_final

155 g * T_final + 150 g *T_final = 150 g * 85 C + 155 g * 26 C

T_final * 305 g = 12750 g C + 4030 g C

T_final * 305 g = 16780 g C

T_final  = 16780 g C / 305 g

T final = 55.02 C [ANSWER]