(II) At a given latitude, ocean water in the so-called mixed layer (from the surface to a depth of about $50 \mathrm{~m}$ ) is at approximately the same temperature due to the mixing action of waves. Assume that because of global warming, the temperature of the mixed layer is everywhere increased by $0.5^{\circ} \mathrm{C}$, while the temperature of the deeper portions of the ocean remains unchanged. Estimate the resulting rise in sea level. The ocean covers about $70 \%$ of the Earth's surface.

A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of $5.00 \mathrm{~atm}$ and a volume of $12.0 \mathrm{~L}$ to a final volume of $30.0 \mathrm{~L}$. Find $Q, W$, and $\Delta E_{\text {int }}$.

A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of $5.00 \mathrm{~atm}$ and a volume of $12.0 \mathrm{~L}$ to a final volume of $30.0 \mathrm{~L}$. What are the initial and final temperatures?

If $25.50$ mol of helium gas is at $10\degree\mathrm{C}$ and a gauge pressure of $0.350$ atm, calculate (a) the volume of the helium gas under these conditions, and (b) the temperature if the gas is compressed to precisely half the volume at a gauge pressure of $1.00$ atm.

(II) Estimate the number of moles of water in all the Earth's oceans. Assume water covers $75 \%$ of the Earth to an average depth of $3 \mathrm{~km}$.

In the deep space between galaxies, the density of molecules (which are mostly single atoms) can be as low as 10^6 atoms/m^3, and the temperature is a frigid 2.7 K. What is the pressure? (b) What volume (in m^3 ) is occupied by 1 mol of gas? (c) If this volume is a cube, what is the length of its sides in kilometers?

Make a conjecture about each value or geometric relationship. the product of two odd numbers

A $3.65-\mathrm{mol}$ sample of an ideal diatomic gas expands adiabatically from a volume of $0.1210 \mathrm{~m}^3$ to $0.750 \mathrm{~m}^3$. Initially the pressure was $1.00 \mathrm{~atm}$. Determine the heat lost by the gas. (Assume no molecular vibration.)

A $3.65-\mathrm{mol}$ sample of an ideal diatomic gas expands adiabatically from a volume of $0.1210 \mathrm{~m}^3$ to $0.750 \mathrm{~m}^3$. Initially the pressure was $1.00 \mathrm{~atm}$. Determine the work done on the gas. (Assume no molecular vibration.)

If the ${W} 310 \times 24$ beam is made from steel having an allowable normal stress of $\sigma_{\text {allow }}=150 {MPa}$ and an allowable shear stress of $\tau_{\text {allow }}=60 {MPa}$, determine the maximum cable force $P$ that can safely be supported by the beam.

A heat engine exhausts $7600 \mathrm{~J}$ of heat while performing $2600 \mathrm{~J}$ of useful work. What is the efficiency of this engine?

In an office complex of 1000 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 85% chance that she will be at work tomorrow, and if the employee is absent today, there is a 60% chance that she will be absent tomorrow. Suppose that today there are 760 employees at work. (a) Find the transition matrix for this scenario. (b) Predict the number that will be at work five days from now. (c) Find the steady-state vector.

Let x be a binomial random variable with n=100 and p=.2. Find approximations to these probabilities: a. P(x$\gt$22) b. P(x$\geq$22) c. P(20$\lt$x$\lt$25) d. P(x$\leq$25)

Diego Chavez has a charge account with a previous $112.34 balance, a$3.55 finance charge, new purchases of $87.50 and$115.60, a $100.00 payment, and a$25.00 credit. What is the new balance?