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Chapter 10: Problem 8

The temperature difference between the inside and the outside of a home on a cold winter day is \(57.0^{\circ} \mathrm{F}\). Express this difference on (a) the Celsius scale and (b) the Kelvin scale.

Short Answer

Expert verified
The temperature difference expressed in the Celsius scale is approximately \(13.89^{\circ}C\) and in the Kelvin scale approximately 287.04K

Step by step solution

01

Convert Fahrenheit to Celsius

First, we have to convert the temperature from Fahrenheit to Celsius using the formula: \(T_C = (T_F - 32) * (5/9)\). For \(T_F = 57.0^{\circ} \mathrm{F}\), we get \(T_C = (57.0 - 32) * (5/9) = 13.89^{\circ}C\)
02

Convert Celsius to Kelvin

Next, we can convert the temperature from Celsius to Kelvin, using the formula: \(T_K = T_C + 273.15\). With \(T_C = 13.89^{\circ}C\), we obtain \(T_K = 13.89 + 273.15 = 287.04K\).

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Most popular questions from this chapter

\(\underline{Q C}\) A grandfather clock is controlled by a swinging brass pendulum that is \(1.3 \mathrm{~m}\) long at a temperature of \(20^{\circ} \mathrm{C}\). (a) What is the length of the pendulum rod when the temperature drops to \(0.0^{\circ} \mathrm{C}\) ? (b) If a pendulum's period is given by \(T=2 \pi \sqrt{L / g}\), where \(L\) is its length, does the change in length of the rod cause the clock to run fast or slow?

In a period of \(1.0 \mathrm{~s}, 5.0 \times 10^{23}\) nitrogen molecules strike a wall of area \(8.0 \mathrm{~cm}^{2}\). If the molecules move at \(300 \mathrm{~m} / \mathrm{s}\) and strike the wall head-on in a perfectly elastic collision, find the pressure exerted on the wall. (The mass of one \(\mathrm{N}_{2}\) molecule is \(4.68 \times 10^{-26} \mathrm{~kg}\).)

Before beginning a long trip on a hot day, a driver inflates an automobile tire to a gauge pressure of \(1.80 \mathrm{~atm}\) at \(300 \mathrm{~K}\). At the end of the trip, the gauge pressure has increased to \(2.20\) atm. (a) Assuming the volume has remained constant, what is the tempera- ture of the air inside the tire? (b) What percentage of the original mass of air in the tire should be released so the pressure returns to its original value? Assume the temperature remains at the value found in part (a) and the volume of the tire remains constant as air is released.

Use Avogadro's number to find the mass of a helium atom.

The boiling point of liquid hydrogen is \(20.3 \mathrm{~K}\) at atmospheric pressure. What is this temperature on (a) the Celsius scale and (b) the Fahrenheit scale?
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