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Chapter 17: Problem 117

Careful measurements show that the specific heat of the solid phase depends on temperature (Fig. P17.117). How will the actual time needed for this cryoprotectant to come to equilibrium with the cold plate compare with the time predicted by using the values in the table? Assume that all values other than the specific heat (solid) are correct. The actual time (a) will be shorter; (b) will be longer; (c) will be the same; (d) depends on the density of the cryoprotectant.

Short Answer

Expert verified
The actual time will (b) be longer if the specific heat increases with decreasing temperature.

Step by step solution

01

Understand the problem

We are asked to determine how the actual cooling time of a cryoprotectant will compare with the predicted time if the specific heat of the solid phase depends on temperature.
02

Consider the effect of specific heat

Specific heat is a measure of how much energy is required to change the temperature of a substance. If specific heat varies with temperature, the energy required to reach equilibrium temperature may differ from predictions that assume a constant specific heat.
03

Analyze the impact of a variable specific heat

If the specific heat increases with temperature, more energy is needed to lower the temperature, elongating the process compared to using a constant value. Conversely, if it decreases, less energy is required, potentially reducing the time.
04

Relate to equilibrium time

The time to reach equilibrium is related to the energy exchanged, which depends on specific heat. Because the problem states the table's constant value might not be accurate, consider this variability in the specific heat to answer the effect on time.

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Key Concepts

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

Temperature Dependence
Temperature dependence is a crucial factor in understanding how specific heat functions. The specific heat of a material indicates how much energy is required to increase the temperature of that material by one degree. For some materials, specific heat does not remain constant and can change as the temperature of the material changes.
This dependence means that as the temperature of a cryoprotectant varies, the specific heat may increase or decrease.
  • If the specific heat increases at higher temperatures, more energy will be needed to continue raising the temperature, leading to longer cooling or heating times.
  • Conversely, if the specific heat decreases, less energy will be needed, potentially shortening the time needed to change the temperature.
Understanding how specific heat changes with temperature can allow more accurate predictions of how quickly or slowly a material will reach a desired temperature.
Cooling Time
Cooling time refers to how long it takes for a substance to reach the desired thermal equilibrium with its surroundings. This is often influenced by the material's specific heat, which, as mentioned before, can depend on temperature.
In the case of a cryoprotectant, the cooling time is determined by how efficiently heat is exchanged between the cryoprotectant and the cold plate.
  • An increase in specific heat implies that more energy is needed to lower temperatures, possibly resulting in a longer cooling time than predicted.
  • If specific heat decreases with a drop in temperature, it might speed up the cooling process, shortening the cooling time.
When predicting the cooling time, considering the variable nature of specific heat is essential for accurate assessments.
Equilibrium Temperature
The equilibrium temperature is the final temperature reached when a substance and its surroundings reach thermal balance. For a substance like a cryoprotectant interacting with a cold plate, this means the point at which there is no further net energy exchange.
The process to reach this equilibrium is dependent on the material properties, such as specific heat, and factors in how specific heat varies with temperature.
  • If a cryoprotectant has a specific heat that decreases with temperature, getting to equilibrium might occur more rapidly.
  • In contrast, if the specific heat increases, the journey to equilibrium could take longer due to the need for more energy transfer.
The understanding of these properties helps engineers and scientists design processes to achieve desired temperature changes efficiently.
Cryoprotectant
A cryoprotectant is a substance used to protect biological tissue from freezing damage. This is especially relevant in processes like cryopreservation, where biological specimens are preserved at extremely low temperatures.
The specific heat of a cryoprotectant is important because it determines how the material will respond to changes in temperature.
  • Understanding if its specific heat changes with temperature can help predict how quickly it can be cooled down safely without causing damage.
  • It is crucial for ensuring that the delicate balance of freezing protective biological materials is maintained.
Considering these characteristics is vital for optimizing cryoprotectants and ensuring they perform as required to protect sensitive biological materials during temperature changes.

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Most popular questions from this chapter

A technician measures the specific heat of an unidentified liquid by immersing an electrical resistor in it. Electrical energy is converted to heat transferred to the liquid for 120 s at a constant rate of 65.0 W. The mass of the liquid is 0.780 kg, and its temperature increases from 18.55\(^\circ\)C to 22.54\(^\circ\)C. (a) Find the average specific heat of the liquid in this temperature range. Assume that negligible heat is transferred to the container that holds the liquid and that no heat is lost to the surroundings. (b) Suppose that in this experiment heat transfer from the liquid to the container or surroundings cannot be ignored. Is the result calculated in part (a) an overestimate or an underestimate of the average specific heat? Explain.

A machinist bores a hole of diameter 1.35 cm in a steel plate that is at 25.0\(^\circ\)C. What is the cross-sectional area of the hole (a) at 25.0\(^\circ\)C and (b) when the temperature of the plate is increased to 175\(^\circ\)C? Assume that the coefficient of linear expansion remains constant over this temperature range.

Consider a poor lost soul walking at 5 km/h on a hot day in the desert, wearing only a bathing suit. This person's skin temperature tends to rise due to four mechanisms: (i) energy is generated by metabolic reactions in the body at a rate of 280 W, and almost all of this energy is converted to heat that flows to the skin; (ii) heat is delivered to the skin by convection from the outside air at a rate equal to \(k'A{_s}{_k}{_i}{_n}(T{_a}{_i}{_r} - T{_s}{_k}{_i}{_n})\), where \(k'\) is 54 J/h \(\cdot\) C\(^\circ\) \(\cdot\) m\(^2\), the exposed skin area \(A{_s}{_k}{_i}{_n}\) is 1.5 m\(^2\), the air temperature \(T{_a}{_i}{_r} \)is 47\(^\circ\)C, and the skin temperature \(T{_s}{_k}{_i}{_n}\) is 36\(^\circ\)C; (iii) the skin absorbs radiant energy from the sun at a rate of 1400 W/m\(^2\); (iv) the skin absorbs radiant energy from the environment, which has temperature 47\(^\circ\)C. (a) Calculate the net rate (in watts) at which the person's skin is heated by all four of these mechanisms. Assume that the emissivity of the skin is \(e\) = 1 and that the skin temperature is initially 36\(^\circ\)C. Which mechanism is the most important? (b) At what rate (in L/h) must perspiration evaporate from this person's skin to maintain a constant skin temperature? (The heat of vaporization of water at 36\(^\circ\)C is \(2.42 \times 10{^6}\) J/kg.) (c) Suppose instead the person is protected by light-colored clothing \((e \approx 0)\) so that the exposed skin area is only 0.45 m\(^2\). What rate of perspiration is required now? Discuss the usefulness of the traditional clothing worn by desert peoples.

You are asked to design a cylindrical steel rod 50.0 cm long, with a circular cross section, that will conduct 190.0 J/s from a furnace at 400.0\(^\circ\)C to a container of boiling water under 1 atmosphere. What must the rod鈥檚 diameter be?

(a) Calculate the one temperature at which Fahrenheit and Celsius thermometers agree with each other. (b) Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each other.
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