Thermodynamics -- Calculations for heating water up

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SUMMARY

The discussion focuses on calculating the time required for water in a thermal flask to cool from 90°C to 55°C in a room at 20°C. Key parameters include the flask's outer radius of 5 cm, height of 25 cm, and a thermal resistance (R) of 0.5 Km²/W. The user attempts to apply the heat transfer equation but struggles with the integration process and determining the correct values for the initial and final temperatures. The conversation highlights the need for clarity on the differential equation and initial conditions involved in the cooling process.

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  • Familiarity with differential equations and their applications in thermal calculations.
  • Knowledge of specific heat capacity, with values such as a = 942.5 and c = 4190.
  • Experience with thermal resistance concepts in heat transfer.
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Homework Statement
nvm
Relevant Equations
nvm
A thermal flask with water of temperature 90c is placed out in room temperature 20c, sealed. How long before it reaches 55c?

outer radius and height: 5cm, 25cm

volume of water is 1litre.

R = 0.5 Km2/W

using this equation to solve it combining these two and integrating with respect to T.

ending up with this function. T0 for the original temp inside flask, and putting 55 for Th
Using a= 942.5, c = 4190, and m = 1. Not sure how I am suppose to use this because every answer i get seems weird

The actual formula is for calculating time for water to heat up to its surroundings so I am guessing i need to shuffle the values
 
Last edited:
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This is done pretty incorrectly. What value is TH supposed to be? What is the differential equation that you should be solving? What is the initial condition? What is the final temperature?
 
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