What would be the final temperature if 54.7 g of H₂O at 32.3°C was added to 38.2 g of H₂O at 89.5°C? (Assume no loss of heat to the surroundings.)

A) 60.9°C
B) 61.0°C
C) 61.1°C
D) 61.2°C

Question

High School

We appreciate your visit to What would be the final temperature if 54 7 g of H₂O at 32 3 C was added to 38 2 g of H₂O at. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Answer :

asarwar asarwar · Answer 1 · 2024-12-06T18:54:47-05:00

The final temperature after mixing is approximately 55.3°C. None of the given options is answer.

Given:

- Mass of the first sample (m1) = 54.7 g

- Initial temperature of the first sample (T1) = 32.3°C

- Mass of the second sample (m2) = 38.2 g

- Initial temperature of the second sample (T2) = 89.5°C

We'll use the principle of conservation of energy, assuming no heat loss to the surroundings. We'll use the formula:

m1 * c * (T[tex]_f[/tex] - T1) = -m2 * c * (T[tex]_f[/tex]- T2)

where:

- m1 and T1 are the mass and initial temperature of the first substance,

- m2 and T2 are the mass and initial temperature of the second substance,

- c is the specific heat capacity of the substances (assumed to be the same for water),

- T[tex]_f[/tex] is the final temperature.

Substituting the given values into the formula:

54.7 * 1 * (T[tex]_f[/tex] - 32.3) = -38.2 * 1 * (T[tex]_f[/tex] - 89.5)

54.7 * (T[tex]_f[/tex] - 32.3) = -38.2 * (T[tex]_f[/tex] - 89.5)

Now, solve for T[tex]_f[/tex]:

54.7 * T[tex]_f[/tex]- 54.7 * 32.3 = -38.2 * T[tex]_f[/tex] + 38.2 * 89.5

93.9 * T[tex]_f[/tex] = 5191.10

T[tex]_f[/tex] ≈ 55.3°C

So, the final temperature after mixing is approximately 55.3°C. None of the given options is answer.