Question

Problem #1: Power and temperature change

You are working with a group investigating biological mechanisms that determine a predisposition to obesity. Your assignment is to measure the rate that energy is output by certain types of cells when a nutrient is introduced. To begin this study, you have decided to use a calorimetric technique. A culture of cells with the appropriate nutrient is placed inside a closed container. That container is submerged in a water bath and you measure the rate that the temperature of the bath changes. To calibrate the apparatus, you decide to use a resistor connected across a known voltage as a power source. You know that the power output by the resistor is just the current through the resistor times the voltage across the resistor. You then will compare that power to the rate that the internal energy of the water bath changes by measuring its temperature as a function of time. To accomplish this calibration, you calculate the rate of temperature change as a function of the voltage across the resistor, the current through the resistor, the specific heat of the water, and the mass of the water. You know that even with good insulation, your apparatus will transfer some energy to the outside and your measurements will allow you to correct for this.

Equipment You have a constant voltage power supply, banana wires, alligator clips, a resistive heating apparatus, digital multimeters (DMMs), digital thermometer, and water containers.

Pre-lab: Warm-up and prediction Warmup: It is useful to have an organized problem-solving strategy. The following questions will help with your prediction and the analysis of your data. 1.Make a sketch of the situation. Identify and label the quantities you can measure or look up. Write down the general conservation of energy equation and decide how it will apply to this situation.

2.Identify your system. Decide on the initial time for which you want to calculate the energy of yoursystem and draw the system. Write down the expression for the energy of your system at that time. Decide on the final time for which you want to calculate the energy of your system and draw it. Write down the expression for the energy of your system at that time. Write down an expressionfor any energy transferred to or from your system. Identify the energy transfer on your drawing and whether the terms represent energy input or energy output for your system. 3.Write an equation that associates the change in energy of the liquid with its change in temperature. Write an equation that gives the rate that energy is output by the filament (power = voltage x current; both voltage and current are quantities that you can measure in this experiment).

4.Determine if any of the energy inputs into the systm are small enough to be neglected. Determine if any of the energy outputs from the system are small enough to be neglected. Write down the conservation of energy equation specifically for this situation.

5.Assuming that nothing but electricity transfers energy to or from your system, calculate the change in the temperature of the liquid between your initial and final times. Using this, write an expression that gives the change in temperature of the liquid as a function of time. Sketch a graph 37°C representing this function and write down how you can determine the power transferred from your system in other ways that you have neglected.

Answer 1