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Chapter 1: Q. 1.30 (page 20)

Put a few spoonfuls of water into a bottle with a tight lid. Make sure everything is at room temperature, measuring the temperature of the water with a thermometer to make sure. Now close the bottle and shake it as hard as you can for several minutes. When you're exhausted and ready to drop, shake it for several minutes more. Then measure the temperature again. Make a rough calculation of the expected temperature change, and compare.


Short Answer

Expert verified

Temperature will change due to kinetic energy of molecules.

Step by step solution

01

Given information

Few spoonfuls of water into a bottle with a tight lid.

02

Explanation

Temperature can't change (neither increased nor decreased) without any external factors (heat supply or heat absorption) . Temperature is related to the kinetic energy of the molecules.

When the bottle is kept in the room temperature, then its temperature will be say 25oC.

And when the bottle is shaken for couple of minutes, then its temperature is measured with thermometer. In this case, temperature will be increased due to the kinetic energy of molecules increases during shaking. This change in kinetic energy of molecule causes a change in temperature.


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Most popular questions from this chapter

Consider a uniform rod of material whose temperature varies only along its length, in the xdirection. By considering the heat flowing from both directions into a small segment of length 螖x

derive the heat equation,

鈭�T鈭�t=K鈭�2T鈭�x2

where K=kt/c蚁i, cis the specific heat of the material, and 蚁is its density. (Assume that the only motion of energy is heat conduction within the rod; no energy enters or leaves along the sides.) Assuming that Kis independent of temperature, show that a solution of the heat equation is

T(x,t)=T0+Ate鈭�x2/4Kt,

where T0is a constant background temperature and Ais any constant. Sketch (or use a computer to plot) this solution as a function of x, for several values of t. Interpret this solution physically, and discuss in some detail how energy spreads through the rod as time passes.

Problem 1.36. In the course of pumping up a bicycle tire, a liter of air at atmospheric pressure is compressed adiabatically to a pressure of 7 atm. (Air is mostly diatomic nitrogen and oxygen.)

(a) What is the final volume of this air after compression?

(b) How much work is done in compressing the air?

(c) If the temperature of the air is initially300K , what is the temperature after compression?

Measured heat capacities of solids and liquids are almost always at constant pressure, not constant volume. To see why, estimate the pressure needed to keep Vfixed as Tincreases, as follows.

(a) First imagine slightly increasing the temperature of a material at constant pressure. Write the change in volume,dV1, in terms of dTand the thermal expansion coefficient 尾introduced in Problem 1.7.

(b) Now imagine slightly compressing the material, holding its temperature fixed. Write the change in volume for this process, dV2, in terms of dPand the isothermal compressibility 魏T, defined as

魏T鈮�鈭�1V鈭�V鈭�PT

(c) Finally, imagine that you compress the material just enough in part (b) to offset the expansion in part (a). Then the ratio of dPtodTis equal to (鈭�P/鈭�T)V, since there is no net change in volume. Express this partial derivative in terms of 尾and魏T. Then express it more abstractly in terms of the partial derivatives used to define 尾and魏T. For the second expression you should obtain

鈭�P鈭�TV=鈭�(鈭�V/鈭�T)P(鈭�V/鈭�P)T

This result is actually a purely mathematical relation, true for any three quantities that are related in such a way that any two determine the third.

(d) Compute 尾,魏T,and(鈭�P/鈭�T)Vfor an ideal gas, and check that the three expressions satisfy the identity you found in part (c).

(e) For water at 25鈭�C,尾=2.57脳10鈭�4K鈭�1and魏T=4.52脳10鈭�10Pa鈭�1. Suppose you increase the temperature of some water from 20鈭�Cto30鈭�C. How much pressure must you apply to prevent it from expanding? Repeat the calculation for mercury, for which (at25鈭�C)尾=1.81脳10鈭�4K鈭�1and魏T=4.04脳10鈭�11Pa鈭�1

Given the choice, would you rather measure the heat capacities of these substances at constant vor at constant p?

Does it ever make sense to say that one object is "twice as hot" as another? Does it matter whether one is referring to Celsius or Kelvin temperatures? Explain.

Give an example of a process in which no heat is added to a system, but its temperature increases. Then give an example of the opposite: a process in which heat is added to a system but its temperature does not change.
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