Problem #1: Power and temperature change
You are working with a group investigating biological mechanismsthat determine a predisposition to obesity. Your assignment is tomeasure the rate that energy is output by certain types of cellswhen a nutrient is introduced. To begin this study, you havedecided to use a calorimetric technique. A culture of cells withthe appropriate nutrient is placed inside a closed container. Thatcontainer is submerged in a water bath and you measure the ratethat the temperature of the bath changes.
To calibrate the apparatus, you decide to use a resistorconnected across a known voltage as a power source. You know thatthe power output by the resistor is just the current through theresistor times the voltage across the resistor. You then willcompare that power to the rate that the internal energy of thewater bath changes by measuring its temperature as a function oftime. To accomplish this calibration, you calculate the rate oftemperature change as a function of the voltage across theresistor, the current through the resistor, the specific heat ofthe water, and the mass of the water. You know that even with goodinsulation, your apparatus will transfer some energy to the outsideand your measurements will allow you to correct for this.
Equipment: You have a constant voltage power supply, bananawires, alligator clips, a resistive heating apparatus, digitalmultimeters (DMMs), digital thermometer, and water containers.
Pre-lab: Warm-up and prediction Warmup: It is useful to have anorganized problem-solving strategy. The following questions willhelp with your prediction and the analysis of your data. 1.Make asketch of the situation. Identify and label the quantities you canmeasure or look up. Write down the general conservation of energyequation and decide how it will apply to this situation.
2.Identify your system. Decide on the initial time for which youwant to calculate the energy of yoursystem and draw the system.Write down the expression for the energy of your system at thattime. Decide on the final time for which you want to calculate theenergy of your system and draw it. Write down the expression forthe energy of your system at that time. Write down an expressionforany energy transferred to or from your system. Identify the energytransfer on your drawing and whether the terms represent energyinput or energy output for your system.
3.Write an equation that associates the change in energy of theliquid with its change in temperature. Write an equation that givesthe rate that energy is output by the filament (power = voltage xcurrent; both voltage and current are quantities that you canmeasure in this experiment).
4.Determine if any of the energy inputs into the systm are smallenough to be neglected. Determine if any of the energy outputs fromthe system are small enough to be neglected. Write down theconservation of energy equation specifically for thissituation.
5.Assuming that nothing but electricity transfers energy to orfrom your system, calculate the change in the temperature of theliquid between your initial and final times. Using this, write anexpression that gives the change in temperature of the liquid as afunction of time. Sketch a graph 37°C representing this functionand write down how you can determine the power transferred fromyour system in other ways that you have neglected.
