Temperature

4-1

At what temperature do the following pairs of scales give the same reading: (a) Fahrenheit and Celsius, (b) Fahrenheit and Kelvin and (c) Celsius and Kelvin?

4-2

Soon after the earth formed, heat released by the decay of radioactive elements raised the average internal temperature from 300 to 3000 K, at about which value it remains today. Assuming an average coefficient of volume expansion of $3\times 10^{-5} \rm K^{-1}$, by how much has the radius of the earth increased since its formation?

4-3

The distance between the towers of the main span of the Golden Gate Bridge near San Francisco is 4200 feet (see Fig. 5). The sag of the cable halfway between the towers at $50 \rm ^oF$ is 470 feet. Take $\alpha = 6.5\times 10^{-6}/ \rm F$ for the cable and compute (a) the change in length of the cable and (b) the change in sag for a temperature change from 10 to $90 \rm ^o F$. Assume no bending or separation of the towers and a parabolic shape for the cable.

Figure 5: Prob 4-3

4-4

9 grams of water are placed in 2.00-L pressure cooker and heated to $500 \rm ^o C$. What is the pressure inside the container if no gas escapes?

4-5

A spherical weather balloon is designed to expand to a maximum radius of 20.0 metres when in flight at its working altitude, where the air pressure is 0.0300 atm and the temperature is 200 K. If the balloon is filled at atmospheric pressure and 300 K what is its radius at liftoff?

4-6

A cylinder is closed by a piston connected to a spring of constant $2.00\times 10^3  \rm N/m$ (see Fig. 6). While the spring is relaxed, the cylinder is filled with 5.00 L of gas at a pressure of 1.00 atm and a temperature of $20.0 \rm ^o C$. (a) If the piston has a cross-sectional area of $0.010  \rm m^2$ and a negligible mass, how high will it rise when the temperature is increased to $250 \rm ^o C$? (b) What is the pressure of the gas at $250 \rm ^o C$?

Figure 6: Prob 4-6