Find the temperature of Liquid A after 12 minutes

In summary: The first entry is obviously (ΔT)1 = T2 - T1. What about the ith entry? Is it (ΔT)i = Ti+1 - Ti or, as OP surmised, (ΔT)i = Ti+1 - T1? The former set of "instantaneous slope" entries is probably more useful because the average gives an approximate value of the slope that could be verified with a linear fit.The first entry is obviously (ΔT)1 = T2 - T1. What about the ith entry? Is it (ΔT)i = Ti+1 - Ti or, as OP surmised, (
  • #1
Richie Smash
293
15

Homework Statement


A liquid A initially at temperature T1= 28.4°C, is heated by an immersion heater in container. The resulting temperature T2 is recorded at 1 minute intervals and the following results obtained.
(I will post a picture)
(a) Complete the table by computing temperature changes ΔT=T2-T1
I've done this and the missing values are: 7.6, 14.7, 24.1, 32.1,40.6,46.7,55.9 degrees Celsius.
(b) Plot a graph of ΔT against time (t). I've also done this.
(c) Find the slope S of the graph, I've also done this and I got 8.33.
(d) Cp the Specific Heat capacity of the liquid is related to the slope S by : Cp=2000/S J Kg-1K-1.
Find the Specific Heat Capacity of the Liquid.
I've also done this and got 240.1J Kg-1K-1.
(e) What would be the temperature of the liquid after 12 minutes?
This is where I'm stuck.

Homework Equations


Eh=m*C*ΔT

The Attempt at a Solution


I'm really stuck, I was thinking now I have the specific heat capacity i could find the energy supplied, then relate that to the temperature change but I don't have the mass. They basically want X°C-28.4°C and that would give you the temperature change after 12 minutes then simply add to the initial temperature to get the final.

But I'm pretty unsure I've been racking my brain looking for formulas linking temperature and time.
 

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  • #2
Richie Smash said:
(e) What would be the temperature of the liquid after 12 minutes?
This is where I'm stuck.
In part (c) you didn't include the units for the slope. This should help with answering part (e). Interpret what the slope is telling you.
 
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  • #3
The unit would then be degrees Celsius per minute?
 
  • #4
Richie Smash said:
The unit would then be degrees Celsius per minute?
Yes.
 
  • #5
Wait, so it's as simple as doing 8.33 degrees celsius per min *12 +28.4 to give me 128.36°C
 
  • #6
Richie Smash said:
Wait, so it's as simple as doing 8.33 degrees celsius per min *12 +28.4 to give me 128.36°C
Yes, that looks right. However, I don't know how you got your value of 8.33 Co/min for the slope. It appears to be a little too large.
 
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  • #7
On My graph I drew a line of best fit, so I suppose there was human error involved in finding the gradient.
 
  • #8
Richie Smash said:
On My graph I drew a line of best fit, so I suppose there was human error involved in finding the gradient.
Ok. I think your work looks good.
 
  • #9
How did the graph look?
 
  • #10
Daynea G said:
How did the graph look?
What graph?
 
  • #11
The graph for the work
 
  • #12
Daynea G said:
The graph for the work
I only see one image attached in the thread, the image in post #1. To the right of the image I see part of a sheet of graph paper, but no actual graph.
 
  • #13
Me too that's why I asked
 
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There seems to be an ambiguity as to the entries in the row labeled "Temperature changes ΔT/oC". The first entry is obviously (ΔT)1 = T2 - T1. What about the ith entry? Is it (ΔT)i = Ti+1 - Ti or, as OP surmised, (ΔT)i = Ti+1 - T1? The former set of "instantaneous slope" entries is probably more useful because the average gives an approximate value of the slope that could be verified with a linear fit.
 

Related to Find the temperature of Liquid A after 12 minutes

1. What is the formula for finding the temperature of Liquid A after 12 minutes?

The formula for finding the temperature of Liquid A after 12 minutes would depend on various factors such as the initial temperature of the liquid, the surrounding temperature, and the specific heat capacity of the liquid. However, a general formula that can be used is Q = mcΔT, where Q is the heat transferred, m is the mass of the liquid, c is the specific heat capacity, and ΔT is the change in temperature.

2. How do I determine the mass of Liquid A?

The mass of Liquid A can be determined by using a scale or balance. Simply place a container on the scale, tare it to zero, and then pour the liquid into the container until the desired amount is reached. The reading on the scale will be the mass of the liquid.

3. What is the specific heat capacity of Liquid A?

The specific heat capacity of Liquid A is a measure of how much heat energy is needed to raise the temperature of 1 gram of the liquid by 1 degree Celsius. This value varies depending on the type of liquid and can be found in reference tables or by conducting experiments.

4. How does the surrounding temperature affect the temperature of Liquid A after 12 minutes?

The surrounding temperature can affect the temperature of Liquid A after 12 minutes by either increasing or decreasing it. If the surrounding temperature is higher than the initial temperature of the liquid, the liquid will absorb heat energy from the surroundings and its temperature will increase. On the other hand, if the surrounding temperature is lower, the liquid will release heat energy to the surroundings and its temperature will decrease.

5. Can I use a thermometer to find the temperature of Liquid A after 12 minutes?

Yes, a thermometer can be used to find the temperature of Liquid A after 12 minutes. However, it is important to note that the thermometer must be able to measure the temperature accurately and that the liquid should be stirred or mixed well to ensure an even distribution of heat throughout the liquid.

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