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Chapter 1: Q 1.5. (page 5)

When you're sick with a fever and you take your temperature with a thermometer, approximately what is the relaxation time?

Short Answer

Expert verified

1 minute.

Step by step solution

01

Given information

One sick person measures the temperature of the body and try to fin out the relaxation time.

02

Calculation

Two objects take time to attain thermal equilibrium. The relaxation time is defined as the time taken by an object to achieve the temperature which is 1etimes of its initial value.

Usually when one takes the temperature by using a thermometer, one should wait around a minute to attain equilibrium & so the relaxation time will be approximate 1 minute.

03

Final answer

The relaxation time will be approximately 1 minute

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Most popular questions from this chapter

Two identical bubbles of gas form at the bottom of a lake, then rise to the surface. Because the pressure is much lower at the surface than at the bottom, both bubbles expand as they rise. However, bubble A rises very quickly, so that no heat is exchanged between it and the water. Meanwhile, bubble B rises slowly (impeded by a tangle of seaweed), so that it always remains in thermal equilibrium with the water (which has the same temperature everywhere). Which of the two bubbles is larger by the time they reach the surface? Explain your reasoning fully.

Calculate the total thermal energy in a gram of lead at room temperature, assuming that none of the degrees of freedom are "frozen out" (this happens to be a good assumption in this case).

For a solid, we also define the linear thermal expansion coefficient, 伪, as the fractional increase in length per degree:

伪鈮�螖L/L螖T
(a) For steel, 伪 is 1.1 x 10-5 K-1. Estimate the total variation in length of a 1 km steel bridge between a cold winter night and a hot summer day.
(b) The dial thermometer in Figure 1.2 uses a coiled metal strip made of two different metals laminated together. Explain how this works.
(c) Prove that the volume thermal expansion coefficient of a solid is equal to the sum of its linear expansion coefficients in the three directions 尾=伪x + 伪y + 伪z. (So for an isotropic solid, which expands the same in all directions, 尾 =3 伪 .)

Even at low density, real gases don鈥檛 quite obey the ideal gas law. A systematic way to account for deviations from ideal behavior is the virial

expansion,

PV鈭�nRT(1+B(T)(V/n)+C(T)(V/n)2+鈰�)

where the functions B(T), C(T), and so on are called the virial coefficients. When the density of the gas is fairly low, so that the volume per mole is large, each term in the series is much smaller than the one before. In many situations, it鈥檚 sufficient to omit the third term and concentrate on the second, whose coefficient B(T)is called the second virial coefficient (the first coefficient is 1). Here are some measured values of the second virial coefficient for nitrogen (N2):

T(K)
B(cm3/mol)
100鈥�160
200鈥�35
300鈥�4.2
4009.0
50016.9
60021.3
  1. For each temperature in the table, compute the second term in the virial equation, B(T)/(V/n), for nitrogen at atmospheric pressure. Discuss the validity of the ideal gas law under these conditions.
  2. Think about the forces between molecules, and explain why we might expect B(T)to be negative at low temperatures but positive at high temperatures.
  3. Any proposed relation between P, V, andT, like the ideal gas law or the virial equation, is called an equation of state. Another famous equation of state, which is qualitatively accurate even for dense fluids, is the van der Waals equation,
    (P+an2V2)(V鈭�nb)=nRT
    where a and b are constants that depend on the type of gas. Calculate the second and third virial coefficients (Band C) for a gas obeying the van der Waals equation, in terms of aand b. (Hint: The binomial expansion says that (1+x)p鈮�1+px+12p(p鈭�1)x2, provided that |px|鈮�1. Apply this approximation to the quantity [1鈭�(nb/V)]鈭�1.)
  4. Plot a graph of the van der Waals prediction for B(T), choosing aand bso as to approximately match the data given above for nitrogen. Discuss the accuracy of the van der Waals equation over this range of conditions. (The van der Waals equation is discussed much further in Section 5.3.)

A frying pan is quickly heated on the stovetop 200鈭�CIt has an iron handle that is 20cmlong. Estimate how much time should pass before the end of the handle is too hot to grab with your bare hand. (Hint: The cross-sectional area of the handle doesn't matter. The density of iron is about7.9g/cm3and its specific heat is 0.45J/g鈰�鈭�C).
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