How much heat ΔQ is consumed to raise the ice temperature

In summary, the conversation discusses the consumption of heat ΔQ required to raise the temperature of ice from Ti = -20 Celsius to the melting point Tf = 0, as well as the time it takes for this process. The equation dQ = cmΔT is used, where c is the heat capacity of water. The estimated value of 2.49 * 10^-21 J is questioned and further calculations are done to determine the correct value, which is approximately 6 J. However, there is some confusion regarding the units and heat capacity used in the calculations.
  • #1
Firben
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1. How much heat ΔQ is consumed to raise the ice temperature from Ti = -20 Celsius to meltingpoint Tf = 0 ? how long does it take ?



2. dQ/dt = H = 300 W

dQ = cmΔT




3 I got it to be 2.49 * 10^-21 J. Is it right ?
 
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  • #2


Firben said:
1. How much heat ΔQ is consumed to raise the ice temperature from Ti = -20 Celsius to meltingpoint Tf = 0 ? how long does it take ?



2. dQ/dt = H = 300 W

dQ = cmΔT




3 I got it to be 2.49 * 10^-21 J. Is it right ?
You will have to provide a bit more information. How much ice are we talking about? Does the heat source provide 300 W?

AM
 
  • #3


I don't know anything about the mass.

c = 1/m * dQ/dt (1)

c = 4190 kJ/kg (heat capacity of water)

Q = mcΔT (2)

From equation (1): m = (dQ/dt)/c (3)

m = 300W/4190 k//kg = 0.0715 kg

(2) Q = (0.0715 kg)(4190 kJ/kg)(273-15-253.15)K <==>

Q = 5.99 =~ 6 J

t = Q/H (4) (heat/power)

t(time) = 6.0 J/300 W = 0.02 J/s = 2 min

Is it right ?
 
  • #4


How did you get the equation (1)?
 
  • #5


I just solved it, an oversight
 
  • #6


The units are wrong. c has units of energy/mass. 1/m(dQ/dt) has units of energy/(mass x time).

Your derivation of m makes no sense. You are using the wrong heat capacity. You have to use the heat capacity of ice, not liquid water. Are you sure you got it solved?

AM
 

FAQ: How much heat ΔQ is consumed to raise the ice temperature

What is the formula for calculating the heat consumed to raise the ice temperature?

The formula for calculating the heat consumed to raise the ice temperature is ΔQ = m * c * ΔT, where m is the mass of the ice, c is the specific heat capacity of ice, and ΔT is the change in temperature.

How do I determine the specific heat capacity of ice?

The specific heat capacity of ice is 2.09 J/g°C. This value can be found in most physics or chemistry textbooks or by conducting experiments.

Is the heat consumed to raise the ice temperature the same as the heat released when the ice melts?

No, the heat consumed to raise the ice temperature is not the same as the heat released when the ice melts. The heat consumed is used to increase the temperature of the ice, while the heat released is the energy needed for the ice to change from a solid to a liquid state.

Does the amount of heat consumed to raise the ice temperature depend on the initial temperature of the ice?

Yes, the amount of heat consumed to raise the ice temperature does depend on the initial temperature of the ice. It takes more energy to raise the temperature of ice that is closer to its melting point than ice that is at a lower temperature.

How can I calculate the heat consumed to raise the ice temperature in a real-life scenario?

In a real-life scenario, you would need to know the mass of the ice, the specific heat capacity of ice, and the change in temperature. You would then use the formula ΔQ = m * c * ΔT to calculate the heat consumed. It's important to note that this calculation may not be exact as there are other factors, such as heat loss to the environment, that can affect the final temperature of the ice.

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