Thermodynamics -- Calculations for heating water up

In summary, a thermal flask with 1 litre of water at 90c is placed in a room with a temperature of 20c. The outer radius and height of the flask are 5cm and 25cm, respectively. Using the equation R = 0.5 Km2/W and integrating with respect to T, the function for calculating the time for the water to heat up to its surroundings is obtained. However, the values given (a=942.5, c=4190, m=1) do not seem to accurately solve the problem. The final temperature is not specified and there is confusion about the values for TH and the differential equation being solved. The thread has been temporarily locked for moderation.
  • #1
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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
 
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  • #2
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?
 
  • #3
Thread locked temporarily for Moderation
 

1. How do you calculate the amount of heat needed to raise the temperature of water?

The amount of heat needed to raise the temperature of water can be calculated using the formula Q = mcΔT, where Q is the heat energy, m is the mass of water, c is the specific heat capacity of water, and ΔT is the change in temperature.

2. What is the specific heat capacity of water?

The specific heat capacity of water is 4.186 joules per gram per degree Celsius (J/g°C). This means that it takes 4.186 joules of energy to raise the temperature of 1 gram of water by 1 degree Celsius.

3. How do you convert between Celsius and Fahrenheit?

To convert from Celsius to Fahrenheit, use the formula F = (C x 9/5) + 32, where F is the temperature in Fahrenheit and C is the temperature in Celsius. To convert from Fahrenheit to Celsius, use the formula C = (F - 32) x 5/9.

4. Can you use the same formula to calculate the heat needed for both liquid and solid water?

No, the specific heat capacity of water changes depending on its state. For liquid water, the specific heat capacity is 4.186 J/g°C, but for solid water (ice), it is 2.108 J/g°C. Therefore, you would need different calculations for heating up liquid and solid water.

5. How does the altitude affect the calculations for heating water?

The altitude can affect the calculations for heating water because the boiling point of water decreases as altitude increases. This means that it takes less energy to heat water at higher altitudes, as it will boil at a lower temperature. However, for small changes in altitude, the effect on the calculations is negligible.

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