As a result of a temperature rise of 38 C°, a bar with a crack at its center buckles upward (see the figure). If the fixed distance Lò is 4.12 m and the coefficient of linear expansion of the bar is 25.0 × 10-6/Co°, find the rise x of the center. Lo Number Units

Show that =3a , by calculating the infinitesimal change in volume dT of a cube with sides of length L when the temperature changes by dT .

Using a numerical integration method such as Simpson's rule, find the fraction of molecules in a sample of oxygen gas at a temperature of 250 K that have speeds between 100 m/s and 150 m/s. The molar mass of oxygen (O2) is 32.0 g/mol. A precision to two significant digits is enough.

A mole of gas has isobaric expansion coefficient dV/dT=R/p and isochoric pressure-temperature coefficient dp/dT=p/T . Find the equation of state of the gas.

The height of the Washington Monument is measured to be 170.00 m on a day when the temperature is 35.0 . What will its height be on a day when the temperature falls to -10.0 ? Although the monument is made of limestone, assume that its coefficient of thermal expansion is the same as that of marble. Give your answer to five significant figures.

What is the ratio of the average translational kinetic energy of a nitrogen molecule at a temperature of 300 K to the gravitational potential energy of a nitrogen-molecule-Earth system at the ceiling of a 3-m-tall room with respect to the same system with the molecule at the floor?

Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20.0 . (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is 60.0 (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. Is this effect significant?

As the very first rudiment of climatology, estimate the temperature of Earth. Assume it is a perfect sphere and its temperature is uniform. Ignore the greenhouse effect. Thermal radiation from the Sun has an intensity (the "solar constant" S) of about 1370 W/m2 at the radius of Earth's orbit. (a) Assuming the Sun's rays are parallel, what area must S be multiplied by to get the total radiation intercepted by Earth? It will be easiest to answer in tens of Earth's radius, R. (b) Assume that Earth reflects about 30% of the solar energy it intercepts. In other words, Earth has an albedo with a value of A=0.3 . In terms of S, and R, what is the rate at which Earth absorbs energy from the Sun? (c) Find the temperature at which Earth radiates energy at the same rate. Assume that at the infrared wavelengths where it radiates, the emissivity e is 1. Does your result show that the greenhouse effect is important? (d) How does your answer depend on the area of Earth?

(a) Find the density in SI units of air at a pressure of 1.00 atm and a temperature of 20 , assuming that air is 78% N2, 21% O2, and 1% Ar, (b) Find the density of the atmosphere on Venus, assuming that it's 96% CO2 and 4% N2, with a temperature of 737 K and a pressure of 92.0 atm.

Find the ratio f(vp)/f(vrms) for hydrogen gas ( M=2.02 g/mol) at a temperature of 77.0 K.