Heat and temperature change in liquid

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SUMMARY

The discussion focuses on calculating the mass of portion C required to achieve a final temperature of 50.0 °C when mixing three portions of the same liquid with different initial temperatures. Portions A and B have equal masses (m) with temperatures of 94.0 °C and 78.0 °C, respectively, while portion C has an unknown mass (mC) and a temperature of 34.0 °C. The correct approach involves applying the principle of conservation of energy, where the heat lost by portions A and B equals the heat gained by portion C, leading to the equation Q = cm(Tf - T0). The solution requires rearranging this equation to express mC in terms of m.

PREREQUISITES
  • Understanding of specific heat capacity and its equation Q = cm(Tf - T0)
  • Basic knowledge of thermal equilibrium and heat transfer principles
  • Ability to manipulate algebraic equations to solve for unknown variables
  • Familiarity with temperature scales and conversions
NEXT STEPS
  • Study the concept of thermal equilibrium in closed systems
  • Learn more about specific heat capacity and its applications in thermodynamics
  • Practice solving heat transfer problems involving multiple substances
  • Explore the implications of heat exchange in real-world scenarios, such as calorimetry
USEFUL FOR

Students studying thermodynamics, physics educators, and anyone interested in understanding heat transfer in liquids.

darw
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Homework Statement



Three portions of the same liquid are mixed in a container that prevents the exchange of heat with the environment. Portion A has a mass m and a temperature of 94.0 °C, portion B also has a mass m but a temperature of 78.0 °C, and portion C has a mass mC and a temperature of 34.0 °C. What must be the mass of portion C so that the final temperature Tf of the three-portion mixture is Tf = 50.0 °C? Express your answer in terms of m; for example, mc = 2.20 m.



Homework Equations



C= (m(Tf-T0))/ Q



The Attempt at a Solution



I attempted to fill in the equation for specific heat for each portion and set them equal to each other, because they are the same liquid/same value for C. This just started me going around in circles; I'm clearly going about this the wrong way.

Could anyone provide some guidance to get me started on the right track? Thanks so much for your time.
 
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sorry, typo.

for the equation I meant: Q = cm (Tf- T0)
 
The heat lost by portion A plus the heat lost by portion B equals the heat gained by portion C if the final temperature is 50 deg C

Write this down as an equation in terms of m, c and the change in temperature for each portion. Rearrange/solve for mC
 

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