Calculate Heating Time for Water Bath to Reach 58.9°C

In summary, the circuit consists of a 20-ohm resistor in 102 g of pure water, initially at 10.1 deg. celsius. The question is how long it will take for the water's temperature to rise to 58.9 deg. celsius, using the heat capacity of water and expressing the answer in seconds with three significant figures. The correct approach is to consider only the power output from the 20 ohm resistor and calculate the current and power using P=I^2R. This is because the total resistance of 30 ohms includes resistors that are not in the water and do not contribute to heating it.
  • #1
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"In the circuit in the figure, a 20-ohm resistor sits inside 102 g of pure water that is surrounded by insulating Styrofoam."

"If the water is initially at temperature 10.1 deg. celsius, how long will it take for its temperature to rise to 58.9 deg. celsius?
Use as the heat capacity of water, and express your answer in seconds using three significant figures."

What I did was finding the total resistance to be equal to 30 ohms.

I then use the mc(delta t) formula; the energy needed is then equal to 20856.144 J. I then equated this to P=V^2/R. I then found the time to be ~ 656 seconds. I'm pretty sure I did it right but MP said I did it wrong. Any suggestions?

Thanks in advance,
 

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  • #2
I found P to be 30 J/s; V is given = 30 volt and total R was found to be 30 ohms. I thought I got it wrong cos of using 30 ohms so I tried using 20 ohms (resistance of the resistor in the water bath) instead of the resistance of the total systemk, but I still got it wrong. Any suggestions? Please help. :cry:
 
  • #3
You're calculating the required heat energy to raise the temperature of the water correctly.

The mistake you are making is in taking the total resistance of the circuit. Remember only the 20 ohm resistor is in the water, so you only want the power output from that one. Try calculating the current through that resistor and applying [tex]P = I^2R[/tex]. Here R should be the 20 ohm resistance only.
 
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  • #4
Thanks for the tip. I got the answer now. It didn't make sense to me though on why it'd take longer to heat when there're less resistors.
 
  • #5
Heart said:
Thanks for the tip. I got the answer now. It didn't make sense to me though on why it'd take longer to heat when there're less resistors.

Because you're only considering the power output from the 20 ohm resistor rather than from the whole 30 ohm resistance in the circuit. The current through the single 20 ohm resistance is equal to that through the "effective" 10 ohm resistance formed by the remaining resistors (since they're in series). When the current is the same, the power output is directly proportional to the resistance. Do you see now ?
 
  • #6
Thanks, I do now. :)
 

FAQ: Calculate Heating Time for Water Bath to Reach 58.9°C

What is a water bath and why is it used in scientific experiments?

A water bath is a device used in scientific experiments to control and maintain a constant temperature for samples or reactions. It consists of a container filled with water that is heated to a specific temperature. This allows for more accurate and consistent results in experiments.

What factors affect the heating time for a water bath?

The heating time for a water bath can be affected by the volume of water, the starting temperature of the water, the type and power of the heating source, and the ambient temperature of the room.

How do you calculate the heating time for a water bath?

The heating time for a water bath can be calculated using the formula: t = (m x ΔT x C) / P, where t is the heating time, m is the mass of water, ΔT is the temperature difference (final temperature - starting temperature), C is the specific heat capacity of water, and P is the power of the heating source.

What is the specific heat capacity of water and why is it important in the calculation?

The specific heat capacity of water is the amount of energy needed to raise the temperature of 1 gram of water by 1 degree Celsius. It is an important factor in the calculation because it determines how much energy is needed to heat the water to a specific temperature.

Are there any safety precautions to consider when using a water bath?

Yes, there are several safety precautions to consider when using a water bath. It is important to use heat-resistant gloves when handling hot containers and to never touch the heating source while it is in use. It is also important to carefully monitor the water level and temperature to prevent spills or overheating. Additionally, make sure to follow any specific safety guidelines provided by the manufacturer of the water bath device.

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