For an ideal gas $C_{V}$ and $C_{p}$ are different because of the work W associated with the volume change for a constant-pressure process. To explore the difference between $C_{V}$ and $C_{p}$ for a liquid or a solid, consider the process in which 5.00 mol of ethanol is warmed from 10.0$^{\circ} \mathrm{C}$ to 60.0$^{\circ} \mathrm{C}$ while the applied pressure remains a constant 1.00 atm. The molar mass of ethanol is M=46.1 g/mol. What is the mass of 5.00 mol of ethanol?

A pneumatic shock absorber consists of a cylinder with a radius of 1.50 cm and a length that varies from a maximum of 30.0 cm to a minimum of 30.0 cm/v, where v is the compression ratio. For ease of manufacturing, v must be an integer. When the cylinder is fully extended and cooled, the air inside has an ambient pressure of 101 kPa and ambient temperature of 30.0$^{\circ} \mathrm{C}$. A quick adiabatic compression heats the air. The cylinder then expands isothermally until it reaches its maximum length. At that time the length remains fixed and the cylinder cools isochorically, returning to the ambient temperature. How much work is done by the air during a full cycle, in terms of v?

Two moles of an ideal gas are compressed in a cylinder at a constant temperature of $85.0^{\circ} \mathrm{C}$ until the original pressure has tripled. (a) Sketch a $p V$-diagram for this process. (b) Calculate the amount of work done.

Two moles of an ideal gas are compressed in a cylinder at a constant temperature of $65.0^{\circ} \mathrm{C}$ until the original pressure has tripled. (a) Sketch a pV-diagram for this process. (b) Calculate the amount of work done.

Six moles of an ideal gas are in a cylinder fitted at one end with a movable piston. The initial temperature of the gas is $27.0^{\circ} \mathrm{C}$ and the pressure is constant. As part of a machine design project, calculate the final temperature of the gas after it has done $2.40 \times 10^{3} J$ of work.

A light, plastic sphere with mass $m=9.00 \mathrm{~g}$ and density $\rho=4.00 \mathrm{~kg} / \mathrm{m}^3$ is suspended in air by thread of negligible mass.
(b) How much does the tension in the thread change if the temperature of the gas is increased to $35.0\degree \mathrm{C}$ ? Ignore the change in volume of the plastic sphere when the temperature is changed.

A light, plastic sphere with mass m = 9.00 g and density $\rho=4.00 \mathrm{kg} / \mathrm{m}^{3}$ is suspended in air by thread of negligible mass. (a) What is the tension T in the thread if the air is at $5.00^{\circ} \mathrm{C}$ and $\rho=1.00 \mathrm{atm}$? The molar mass of air is 28.8 g/mol. (b) How much does the tension in the thread change if the temperature of the gas is increased to $35.0^{\circ} \mathrm{C}$? Ignore the change in volume of the plastic sphere when the temperature is changed.

Test for relative maxima and minima. Use the second-derivative test, if possible. State whether the relative extrema are also absolute extrema. $y=3 x^{2}+12 x+14$

How many different ways can you make 82 cents using current U.S. currency?

Evaluate the expression. $18-4 \sqrt[3]{8}$

Evaluate the expression. $(\sqrt[3]{-27})^{3}+61$

A photon collides with a moving electron. Can the photon's wavelength change as a result? Explain.

Find the limit. If the limit does not exist, so state, or use the symbol $\infty$ or $-\infty$ where appropriate. $\lim _{x \rightarrow-1} \frac{3 x^{3}-x^{2}}{2 x+1}$

Find the least common denominator of the expressions. $\frac{1}{x}, \frac{1}{x^{2}+3 x}, \frac{1}{x+3}$