PHYS 1401 – General Physics I

Heat and Temperature

Leader: ___________________ Recorder: __________________________

Skeptic: ___________________ Encourager: ________________________

Materials

Immersion Heater

Small Styrofoam cup

Large Styrofoam cup

600 ml beaker, pyrex

Stopwatch

Digital Thermometer

Laptop for graphs

(Graduated cylinder next to sink for measuring water)

Introduction

In this lab we will explore some concepts of heat and its relationship to temperature change.

Safety

In this lab we will make use of immersion heaters. Immersion heaters must be immersed in water before they are plugged in. If you plug them in without first immersing them, they will glow red hot and possibly melt, presenting a considerable risk of burning you and also of possibly starting a fire. Be sure to have the immersion heater plugged in only during the indicated times during the procedure. Also, always make sure that the immersion heater is not immersed beyond the bottom of the plastic handle. (You want it in the water but not too much!)

Procedure

Q1. Use the electronic balance to determine the mass of the small Styrofoam cup. Fill the cup with about 100 ml of water and record the mass again. Determine the mass of the water in the beaker.

mass of cup: _______________

mass of cup + water: ________________

mass of water: _______________

Place the Styrofoam cup into the beaker so that it won’t fall over during the procedure.

Q2. On the handle of the immersion heater is a power rating for the heater. Note that it is given in W for both 120 V and 240 V outlets. Record the power rating for 120 V outlets.

Power rating: ___________

In the following procedure, we will heat the water by turning on the immersion heater in 30 s increments.

Q3. Remember from Ch. 6 that Power = Energy/time. If we solve for energy we obtain Energy = Power x time. Explain how you can use the power rating of the heater to determine how much heat energy is delivered to the water in 30 s.

Q4. Based on your answer to Q3, for each step determine the amount of heat, Q, added to the water in J.

Q = ___________

You want to carry out the following procedure with as little time between steps as possible. Familiarize yourself with the entire procedure before carrying it out. Horizontal lines have been placed to indicate the beginning and end of the procedure.

Q5. Record the initial temperature of the water.

T₀ = ___________

Place the immersion heater into water. And plug it in for 30 s while continuously stirring the water. After 30 s unplug the heater.

Q6. Continue to stir and record the temperature of the water once it has come to a steady value.

T₁ = ___________

Plug the immersion heater in for another 30 s while continuously stirring the water. After 30 s unplug the heater.

Q7. Continue to stir and record the temperature of the water after the second input of heat once it has come to a steady value.

T₂ = ___________

Plug the immersion heater in for another 30 s while continuously stirring the water. After 30 s unplug the heater.

Q8. Continue to stir and record the temperature of the water after the third input of heat once it has come to a steady value.

T₃ = ___________

Plug the immersion heater in for another 30 s while continuously stirring the water. After 30 s unplug the heater.

Q9. Continue to stir and record the temperature of the water after the fourth input of heat once it has come to a steady value.

T₄ = ___________

Plug the immersion heater in for another 30 s while continuously stirring the water. After 30 s unplug the heater.

Q10. Continue to stir and record the temperature of the water after the fifth input of heat once it has come to a steady value.

T₅ = ___________

The heater should be unplugged at this point.

In the table below, record the change in temperature after each input of heat. For instance DT₁ = T₁ – T₀, DT₂ = T₂ – T₁, etc

Step #	DT
1
2
3
4
5

Q11. Was the temperature change roughly constant for each step?

Q12. Did a constant amount of heat input produce a constant temperature change?

Q13. What type of relationship does there appear to be between the amount of heat added and the change in temperature?

Q14. If instead of adding heat, we removed heat. What would be the effect on the temperature?

We will now repeat the procedure for a different mass of water.

Q15. Fill the large Styrofoam cup with 200 ml of water and record the mass of the water + beaker. Determine the mass of the water in the beaker now.

mass of Styrofoam Cup: _______________

mass of cup + water: ________________

mass of water: _______________

Q16. Record the initial temperature of the water.

T₀ = ___________

Place the immersion heater into water. And plug it in for 30 s while continuously stirring the water. After 30 s unplug the heater.

Q17. Continue to stir and record the temperature of the water once it has come to a steady value.

T₁ = ___________

Plug the immersion heater in for another 30 s while continuously stirring the water. After 30 s unplug the heater.

Q18. Continue to stir and record the temperature of the water after the second input of heat once it has come to a steady value.

T₂ = ___________

Plug the immersion heater in for another 30 s while continuously stirring the water. After 30 s unplug the heater.

Q19. Continue to stir and record the temperature of the water after the third input of heat once it has come to a steady value.

T₃ = ___________

Plug the immersion heater in for another 30 s while continuously stirring the water. After 30 s unplug the heater.

Q20. Continue to stir and record the temperature of the water after the fourth input of heat once it has come to a steady value.

T₄ = ___________

Plug the immersion heater in for another 30 s while continuously stirring the water. After 30 s unplug the heater.

Q21. Continue to stir and record the temperature of the water after the fifth input of heat once it has come to a steady value.

T₅ = ___________

The heater should be unplugged at this point.

Q22 Did the amount of heat you added to the water each step change between the two procedures? Explain.

Record the amount of heat added for each step.

Q = ___________

In the table below, record the change in temperature after each input of heat. For instance DT₁ = T₁ – T₀, DT₂ = T₂ – T₁, etc

Step #	DT
1
2
3
4
5

Q23. With twice the mass of the water, did the same amount of heat input produce the same change in temperature as before?

Q24. If the temperature change wasn’t roughly the same, how did it compare to the temperature change when the beaker contained 100 ml of water?

Q25. What does this suggest about the relationship between the change in temperature and the mass of the water in the cup?

The relationship between the heat and the change in temperature is given by

Q = mcDT (1) , where m is the mass and c is a constant which depends on the material called the specific heat (also sometimes called the heat capacity or specific heat capacity.) If we solve for DT we obtain and so we see that the change in temperature is proportional to the amount of heat added, and inversely proportional to the mass.

Data Analysis

We can determine the specific heat of water from the data we have collected.

Q26. For each set of data use Excel or LoggerPro to construct a properly labeled graph of the accumulated amount of heat added vs. the temperature at each step. For instance after 1 step you added 3600 J, after two the accumulated amount was 7200 J and so on.

The form of the graph should be something like Q = mcT + b (1) where b is some y-intercept that has little physical meaning. The point is that you should obtain a line.

Q27. If you examine equation (1), the slope of the line should be a product of two physical constants. What are they?

Q28. Add a best fit line to each graph and record the slope of the line for each line below. Attach the graphs properly labeled.

Q29. From each slope, determine the value of the specific heat of water. Record your results.

Q30. For each value you determined, compared the measured value to the accepted value of 4186 J/kg/°C by finding the percent difference. Be careful about units.

Q31. Were your values close to the accepted value? Identify possible sources of error. Remember don’t use catchalls like human or equipment error. Be specific.