Using the first law of thermodynamics, explain why the total energy of an isolated system is always constant.

Two identical containers each hold 1 mole of an ideal gas at 1 atm. Container A holds a monatomic gas and container B holds a diatomic gas. The gas in each container is compressed at constant pressure to half its original volume. (a) What is the ratio $W_A/W_8$ of the work done on gas A to the work done on gas B? (b) What is the ratio $\Delta U_{A} / \Delta U_{\mathrm{B}}$ of the change in internal energy for gases A and B? (c) What is the ratio $Q_A/Q_B$ of the energy transferred to gases A and B?

According to classical physics, a charge e moving with an acceleration a radiates energy at a rate

$$\frac { d E } { d t } = - \frac { 1 } { 6 \pi \epsilon _ { 0 } } \frac { e ^ { 2 } a ^ { 2 } } { c ^ { 3 } }$$

Show that an electron in a classical hydrogen atom spirals into the nucleus at a rate

$$\frac { d r } { d t } = - \frac { e ^ { 4 } } { 12 \pi ^ { 2 } \epsilon _ { 0 } ^ { 2 } m _ { e } ^ { 2 } c ^ { 3 } } \left( \frac { 1 } { r ^ { 2 } } \right)$$

Why is a person able to remove a piece of dry aluminum foil from a hot oven with bare fingers, whereas a burn results if there is moisture on the foil?

Describe two examples in which the force of friction exerted on an object is in the direction of motion of the object.

Let $\Delta g M$ represent the difference in the gravitational fields produced by the Moon at the points on the Earth’s surface nearest to and farthest from the Moon. Find the fraction $\Delta g M / g$, where g is the Earth’s gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)

Use a total differential to approximate the change in the values of f from P toQ. Compare your estimate with the actual change in f. f(x, y)=

$$x^2$$

+2xy-4x; P(1, 2), Q(1.01, 2.04)

Air approaches a normal shock with $T_{1}$=$-7.5^{\circ} \mathrm{F}$, $p_{1}$=14.7 psia, and $V_{1}$=1750 mph. Determine the speed immediately downstream from the shock and the pressure change across the shock. Calculate the corresponding pressure change for a frictionless, shockless deceleration between the same speeds.

The W and Z bosons were first produced at CERN in 1983 by causing a beam of protons and a beam of antiprotons to meet at high energy. Why was this discovery important?

A beam of monochromatic green light is diffracted by a slit of width 0.550 mm. The diffraction pattern forms on a wall 2.06 m beyond the slit. The distance between the positions of zero intensity on both sides of the central bright fringe is 4.10 mm. Calculate the wavelength of the light.

In his 1798 experiment, Cavendish was said to have “weighed the Earth.” Explain this statement.

The pressure gauge on a tank registers the gauge pressure, which is the difference between the interior pressure and exterior pressure. When the tank is full of oxygen (O2), it contains 12.0 kg of the gas at a gauge pressure of 40.0 atm. Determine the mass of oxygen that has been withdrawn from the tank when the pressure reading is 25.0 atm. Assume the temperature of the tank remains constant.

A certain light truck can go around an unbanked curve having a radius of 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve having a radius of 75.0 m?

An alien spaceship traveling at 0.600c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.800c relative to the mother ship. As measured on the Earth, the spaceship is 0.200 ly from the Earth when the landing craft is launched. What speed do the Earth-based observers measure for the approaching landing craft?