When an ideal gas expands at a constant temperature, $\Delta E=0$ for the change. Why?

What is a spontaneous change? What role does kinetics play in determining the apparent spontaneity of a chemical reaction?

Molecules of an ideal gas have no intermolecular attractions and, therefore, undergo no change in potential energy on expansion of the gas. If the expansion is also at a constant temperature, there is no change in the kinetic energy, so the isothermal (constant temperature) expansion of an ideal gas has $\Delta E=0$. Suppose such a gas expands at constant temperature from a volume of $1.0 \mathrm{~L}$ to $12.0 \mathrm{~L}$ against a constant opposing pressure of $14.0 \mathrm{~atm}$. In units of $L \mathrm{~atm}$, what are $q$ and $w$ for this change? (Hints: Is the system doing work, or is work done on the system? What must be the sum of $q$ and $w$ in this case?)

What is the origin of the name thermodynamics?

Using the results of the above problem, determine the Bernoulli constant as a function of radial coordinate $r$.

Determine the intervals over which the function is increasing, decreasing, or constant.

$$f(x)=\frac{3}{2} x$$

Explain how to determine the volume of a gas at a certain temperature using the proportionality constant, $k$.

Identify the terms, the coefficients, and the constant(s) in the expression $-7 t+6 v+7-19 y$.

Prove $\frac{d}{d x} \ln |a x|=\frac{d}{d x} \ln |x|$ for any constant a.

Let $I_{m,n} = \int_{0}^{1}x^{m}(1-x)^{n}\ dx$ for constant $m,n.$ Show that $I_{m,n} = I_{n,m}.$

Determine the derivatives for the given function. Assume $k$ is a constant.

$$P(t)=e^{2 t}$$

To what do the $A_1, A_3$, and $A_{\mathrm{cm}}$ temperatures refer? Are these temperatures constant?

Explain why the function f and f+C, where C is a constant, have the same derivative properties.

Determine the intervals over which the function is increasing, decreasing, or constant.

$$f(x)=\sqrt{x^2-1}$$