/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 119 To measure the specific heat in ... [FREE SOLUTION] | 91Ó°ÊÓ

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To measure the specific heat in the liquid phase of a newly developed cryoprotectant, you place a sample of the new cryoprotectant in contact with a cold plate until the solution's temperature drops from room temperature to its freezing point. Then you measure the heat transferred to the cold plate. If the system isn't sufficiently isolated from its room-temperature surroundings, what will be the effect on the measurement of the specific heat? (a) The measured specific heat will be greater than the actual specific heat; (b) the measured specific heat will be less than the actual specific heat; (c) there will be no effect because the thermal conductivity of the cryoprotectant is so low; (d) there will be no effect on the specific heat, but the temperature of the freezing point will change.

Short Answer

Expert verified
(a) The measured specific heat will be greater than the actual specific heat.

Step by step solution

01

Understanding the Problem

We need to determine what happens to the measurement of the specific heat of a cryoprotectant when the system isn't fully isolated from its surroundings. Specifically, we must find out if the measured specific heat differs from its actual value under these conditions.
02

Defining Specific Heat

The specific heat capacity is defined as the amount of heat required to change the temperature of one kilogram of a substance by one degree Celsius (or Kelvin). It is important that the system be isolated to ensure accurate measurements, where all heat exchange occurs within the system.
03

Analyzing Non-Isolated Effects

If the system isn't isolated, additional heat from the surroundings can enter the system. This leads to more heat appearing to be absorbed by the substance than actually was from the intended process. Therefore, the calculation for specific heat, which depends on measuring the correct heat transfer, would include this extra heat.
04

Relating to Options

Relate this finding to the multiple-choice options. If extra heat from the surroundings is included in the measurement, it makes it seem that more heat was needed to change the temperature, thus increasing the measured specific heat. This corresponds to option (a): the measured specific heat will be greater than the actual specific heat.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cryoprotectant
A cryoprotectant is a substance used to protect biological material from freezing damage. These substances are crucial in preserving cells, tissues, and organs at low temperatures.
Cryoprotectants work by preventing the formation of ice crystals, which can damage cellular structures. There are two main types:
  • Pentrative cryoprotectants like glycerol that penetrate the cell membranes.
  • Non-penetrative ones such as sugars which work outside of the cells.
When conducting experiments with cryoprotectants, it's vital to know their specific heat. This helps in understanding how much heat energy is needed to change their temperature.
Thermal Isolation
Thermal isolation is crucial when measuring specific heat capacity. It ensures that a system does not exchange heat with its surroundings, leading to more precise measurements.
Without proper isolation, external heat could skew results, making it appear as if more or less heat is involved in the system than actually is. Achieving good thermal isolation can be done by:
  • Using insulating materials like foam or vacuum seals.
  • Ensuring the experimental setup is free from drafts or direct heat sources.
Thermal isolation is essential for accuracy, especially in measuring the specific heat of sensitive materials like cryoprotectants.
Heat Transfer
Heat transfer is the movement of thermal energy from one object or substance to another. It occurs in three ways: conduction, convection, and radiation.
In the context of specific heat measurements:
  • Conduction is most directly related as it involves direct heat transfer from the cryoprotectant to the cold plate.
  • Convection could affect measurements if the surrounding air contributes heat to the system.
  • Radiation is usually minimal but could add subtle influences unless controlled.
Understanding heat transfer mechanisms is key to setting up accurate experiments for specific heat measurement.
Specific Heat Capacity
Specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It's represented as "c" in equations and can be calculated with the formula: \(q = mc\Delta T\), where \(q\) is the heat absorbed, \(m\) is the mass, and \(\Delta T\) is the temperature change.
For cryoprotectants, knowing their specific heat capacity helps in:
  • Determining how they will behave under different temperature conditions.
  • Calculating precise energy requirements for freezing processes.
  • Understanding and predicting their protective efficiency against ice formation.
Accurate specific heat data is fundamental when designing cryopreservation protocols.
Measurement Accuracy
Measurement accuracy is critical in scientific experiments, ensuring the results are valid and reliable. When measuring specific heat, any inaccuracies can lead to errors in data interpretation.
Important factors affecting accuracy include:
  • Calibration of instruments: Ensure all measurement devices are properly calibrated before use.
  • Environmental control: Maintain a stable and controlled environment during experiments to reduce external influences.
  • Data recording procedures: Record data meticulously to minimize human error.
For complex substances like cryoprotectants, small inaccuracies can have significant impacts, leading to incorrect assessments of their properties and effectiveness.

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Most popular questions from this chapter

A 4.00-kg silver ingot is taken from a furnace, where its temperature is 750.0\(^\circ\)C, and placed on a large block of ice at 0.0\(^\circ\)C. Assuming that all the heat given up by the silver is used to melt the ice, how much ice is melted?

A copper pot with a mass of 0.500 kg contains 0.170 kg of water, and both are at 20.0\(^\circ\)C. A 0.250-kg block of iron at 85.0\(^\circ\)C is dropped into the pot. Find the final temperature of the system, assuming no heat loss to the surroundings.

During your mechanical engineering internship, you are given two uniform metal bars \(A\) and \(B\), which are made from different metals, to determine their thermal conductivities. Measuring the bars, you determine that both have length 40.0 cm and uniform cross-sectional area 2.50 cm\(^2\). You place one end of bar \(A\) in thermal contact with a very large vat of boiling water at 100.0\(^\circ\)C and the other end in thermal contact with an ice-water mixture at 0.0\(^\circ\)C. To prevent heat loss along the bar's sides, you wrap insulation around the bar. You weigh the amount of ice initially and find it to be 300 g. After 45.0 min has elapsed, you weigh the ice again and find that 191 g of ice remains. The ice-water mixture is in an insulated container, so the only heat entering or leaving it is the heat conducted by the metal bar. You are confident that your data will allow you to calculate the thermal conductivity \(k_A\) of bar \(A\). But this measurement was tedious-you don't want to repeat it for bar \(B\). Instead, you glue the bars together end to end, with adhesive that has very large thermal conductivity, to make a composite bar 80.0 m long. You place the free end of A in thermal contact with the boiling water and the free end of \(B\) in thermal contact with the ice-water mixture. As in the first measurement, the composite bar is thermally insulated. You go to lunch; when you return, you notice that ice remains in the ice-water mixture. Measuring the temperature at the junction of the two bars, you find that it is 62.4\(^\circ\)C. After 10 minutes you repeat that measurement and get the same temperature, with ice remaining in the ice-water mixture. From your data, calculate the thermal conductivities of bar \(A\) and of bar \(B\).

A carpenter builds a solid wood door with dimensions 2.00 m \(\times\) 0.95 m \(\times\) 5.0 cm. Its thermal conductivity is k = 0.120 W/m \(\cdot\) K. The air films on the inner and outer surfaces of the door have the same combined thermal resistance as an additional 1.8-cm thickness of solid wood. The inside air temperature is 20.0\(^\circ\)C, and the outside air temperature is -8.0\(^\circ\)C. (a) What is the rate of heat flow through the door? (b) By what factor is the heat flow increased if a window 0.500 m on a side is inserted in the door? The glass is 0.450 cm thick, and the glass has a thermal conductivity of 0.80 W/m \(\cdot\) K. The air films on the two sides of the glass have a total thermal resistance that is the same as an additional 12.0 cm of glass.

A thirsty nurse cools a 2.00-L bottle of a soft drink (mostly water) by pouring it into a large aluminum mug of mass 0.257 kg and adding 0.120 kg of ice initially at -15.0\(^\circ\)C. If the soft drink and mug are initially at 20.0\(^\circ\)C, what is the final temperature of the system, assuming that no heat is lost?

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