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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

A frying pan is quickly heated on the stovetop 200∘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⋅∘C).

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.

Your 200 g cup of tea is boiling-hot. About how much ice should you add to bring it down to a comfortable sipping temperature of 65°C? (Assume that the ice is initially 65°C. The specific heat capacity of ice isrole="math" localid="1650146844935" 0.5cal/g°C.

In analogy with the thermal conductivity, derive an approximate formula for the diffusion coefficient of an ideal gas in terms of the mean free path and the average thermal speed. Evaluate your formula numerically for air at room temperature and atmospheric pressure, and compare to the experimental value quoted in the text. How does D depend on T, at fixed pressure?

In Problem 1.16 you calculated the pressure of the earth’s atmosphere as a function of altitude, assuming constant temperature. Ordinarily, however, the temperature of the bottommost 10-15 km of the atmosphere (called the troposphere) decreases with increasing altitude, due to heating from the ground (which is warmed by sunlight). If the temperature gradient |dT/dz|exceeds a certain critical value, convection will occur: Warm, low-density air will rise, while cool, high-density air sinks. The decrease of pressure with altitude causes a rising air mass to expand adiabatically and thus to cool. The condition for convection to occur is that the rising air mass must remain warmer than the surrounding air despite this adiabatic cooling.

a. Show that when an ideal gas expands adiabatically, the temperature and pressure are related by the differential equation

dTdP=2f+2TP

b. Assume that dT/dzis just at the critical value for convection to begin so that the vertical forces on a convecting air mass are always approximately in balance. Use the result of Problem 1.16(b) to find a formula for dT/dzin this case. The result should be a constant, independent of temperature and pressure, which evaluates to approximately –10°C/km. This fundamental meteorological quantity is known as the dry adiabatic lapse rate.
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