Specific heat capacity, Q = mcθ

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SUMMARY

The discussion centers on the calculation of final temperature using the specific heat capacity formula Q = mcθ, where the specific heat capacity of water is 4200 J/kg °C. The participant initially calculated the final temperature as 23.33°C, but the correct answer was confirmed to be 30°C. The conversation highlights that the assumption of no heat loss to the surroundings is critical for accurate results, and it notes that while the heat capacity of water varies slightly with temperature, this variation does not significantly affect the final temperature in this context.

PREREQUISITES
  • Understanding of the specific heat capacity formula Q = mcθ
  • Knowledge of the specific heat capacity of water, c = 4200 J/kg °C
  • Basic principles of thermal equilibrium
  • Familiarity with numerical integration techniques for temperature-dependent properties
NEXT STEPS
  • Study the implications of heat loss in thermal calculations
  • Explore the effects of temperature on the specific heat capacity of various substances
  • Learn about numerical integration methods for analyzing heat transfer
  • Investigate real-world applications of specific heat capacity in engineering
USEFUL FOR

Students in physics or engineering courses, educators teaching thermodynamics, and professionals involved in thermal management or heat transfer analysis.

a129

Homework Statement


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Here is the original question (just read the English version).

Homework Equations


Q = mcθ
Specific heat capacity of water, c = 4200 J/kg °C

The Attempt at a Solution


I did Q_(absorbed) = Q_(released)
mcθ = mcθ
mθ = mθ

And I solved for the final temperature, which is 23.33°C. However the correct answer here is A. I'm pretty sure this question is assuming that there is no heat lost to the surroundings.
Thanks!
 

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a129 said:
However the correct answer here is A.
No it isn't. It is C. (You are correct.)
 
Orodruin said:
No it isn't. It is C. (You are correct.)

Thank you!
 
Note that this is true even if you take into account that the heat capacity of water changes slightly decreases with temperature. (It does not change enough for the final temperature to deviate significantly from 23.33 °C.)

Here is a plot of the heat added to the initially 10 °C water and the heat lost by the initially 30 °C water:
upload_2017-11-4_8-46-49.png

The coloured lines are numerical integrations of the tabulated temperature dependent heat capacity of water. The dotted black lines represent the approximation of the heat capacity being 4.2 kJ/kg K. (I used 500 g and 1 kg masses, but only the proportion is relevant for the intersection point in T)
 

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