Measuring Thermodynamic Efficiency

The voltage generated by the Peltier Device represents work done by the flow of heat from a hot to a cold reservoir (a "reservoir" is a "vast storage tank" which can gain or lose heat without changing temperature). We can compute the experimental efficiency as the ratio of the output power to the input power, and can use the reservoir temperatures to calculate the Carnot efficiency

eCarnot = 1 - Tc / Th,

where T c is the temperature of the cold reservoir and T h is the temperature of the hot one (both in Kelvin). eCarnot applies for any process which is reversible and can be modeled using heat transfer to and from reservoirs.

We will use the Thermal Efficiency Apparatus, a 12V 2.5A DC power supply, 3 kg ice, a bucket, water, an ohmmeter, an ammeter, two voltmeters and wire.

Name:

Lab Partners:

When entering numeric data, use exponentials: ie., 1.6 * 10-19 = 1.6E-19.

Procedure

  1. Place the ice in the bucket and cover with water. Connect the pump power supply and place the tubes in the water-ice bucket.

  2. Connect the meters and the power supply as shown (heat engine mode:)

    The power supply is connected to the heating resistor, and the other voltmeter is connected to the load resistor.

  3. Turn the power supply on, and set it for 8 volts. Flip the toggle switch near the ohmmeter connection to the right to record Th (to the left for Tc.) Th should not be above 80 degrees C for more than 5 minutes. Read the temperature from the chart on the apparatus, which translates the thermistor resistance into temperature. Interpolate where necessary.

  4. Measure Th and Tc repeatedly, until they come to equilibrium. This may take 5 to 10 minutes. You do not need to record the interim values. Record the equilibrium temperatures and the voltages and current:
    Rc = kW Rh = kW
    RLow, c = kW RLow, h = kW
    RHigh, c = kW RHigh, h = kW
    TLow, c = C TLow, h = C
    THigh, c = C THigh, h = C
    Tc = C Th = C

    V = V I = A
    Vload = V

Analysis

  1. From step 4, calculate the power supplied to the 2 ohm load:
    Pload = Vload2 / R
    (actually, R = 2.2). This is the portion of the power which is used to do work. Divide by the power supplied by the power supply:
    P = V I
    which is the total power used by the engine. The experimental efficiency is then
    eexp = Pload / P

    =

    Compare with the Carnot efficiency computed from the temperatures (in Kelvin!) of the reservoirs:
    eCarnot =

©2004, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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