A portable coffee heater supplies a potential difference of 12.0 V across a Nichrome heating element with a resistance of $2.00 \Omega$. How many minutes would it take to heat 1.00 kg of coffee from $20.0^{\circ} \mathrm{C}$ to $50.0^{\circ} \mathrm{C}$ with this heater? Coffee has a specific heat of $4184 \mathrm{J} /\left(\mathrm{kg} \cdot^{\circ} \mathrm{C}\right)$. Neglect any energy losses to the environment.

Consider an ideal gas-turbine cycle with two stages of compression and two stages of expansion. The pressure ratio across each stage of the compressor and turbine is 3. The air enters each stage of the compressor at 300 K and each stage of the turbine at 1200 K. Determine the back work ratio and the thermal efficiency of the cycle, assuming (a) no regenerator is used and (b) a regenerator with 75 percent effectiveness is used. Use variable specific heats.

Identify the computer fraud and abuse technique used in each of the following actual examples of computer wrongdoing.

s. Zeus records log-in information when the user of the infected computer logs into a list of target websites, mostly banks and other financial institutions. The user’s data is sent to a remote server where it is used and sold by cyber criminals. The new version of Zeus will significantly increase fraud losses, given that 30% of Internet users bank online.

A company grows in value by 10% each year, and also gains 20% of a growing market estimated at 100 e$^{0.1 t}$ million dollars, where t is the number of years that the company has been in business. Therefore, the value y(t) of the company (in millions of dollars) satisfies

y' =0.1 y+20 e$^{0.1 t}$

y(0) =5

a. Solve this differential equation and initial condition to find a formula for the value of the company after t years.

b. Use your solution to find the value of the company after 2 years.

Suppose you build a rural house where you need to run a pipe to the nearest water supply, which is fortunately at an elevation of about 1000 m above that of your house. The pipe will be 6.0 km long (the distance to the water supply), and the gage pressure at the water supply is 1000 kPa. You require a minimum of 3.0 gal/min of water when the end of your pipe is open to the atmosphere. To minimize cost, you want to buy the smallest-diameter pipe possible. The pipe you will use is extremely smooth. (a) Find the total head loss from the pipe inlet to its exit. Neglect any minor losses due to valves, elbows, entrance lengths, and so on, since the length is so long here and major losses dominate. Assume the outlet of the pipe is open to the atmosphere. (b) Which is more important in this problem, the head loss due to elevation difference or the head loss due to pressure drop in the pipe? (c) Find the minimum required pipe diameter.

Assume that the only exchanges of heat occur between the body and water.

A $50\mathrm{-lb}$ iron ball is heated to $200^{\circ} \mathrm{F}$ and is then immediately plunged into a vessel containing $100 \mathrm{lb}$ of water whose temperature is $40^{\circ} \mathrm{F}$. The specific heat of iron is $0.11.$ (a) Find the temperature of the body as a function of time. Hint. The quantity of hest lost by the iron body in time $t$ is $50(0.11)$ ($200 -T_B$ ), where $T_B$ is its temperature at the end of time $t$. The quantity of heat gained by the water-remember the specific heat of water is oneis $100(1)\left(T_W-40\right)$, where $T_W$ is the temperature of the water at the end of time $\ell$. Since the heat gained by the water is equal to the heat lost by the ball, $50(0.11)\left(200-T_B\right)=100\left(T_W-40\right)$. Solve for $T_W$ snd substitute this value for $T_M$ in (15.3). Solve for $T_B$. (b) Find the common temperature approached by body and water as $t \rightarrow \infty$.

In the given system $d=25 \mathrm{~cm}, D=40 \mathrm{~cm}$, and the head loss from the venturi meter to the end of the pipe is given by $h_L=0.9 V^2 / 2 g$, where $V$ is the velocity in the pipe. Neglecting all other head losses, determine what head $H$ will first initiate cavitation if the atmospheric pressure is $100 \mathrm{kPa}$ absolute. What will be the discharge at incipient cavitation? Suppose $\alpha=1.0$ at all locations.

"A cyclist intends to cycle up a $7.50^{\circ}$ hill whose vertical height is $125 \text{~m}$. The pedals turn in a circle of diameter $36.0 \text{~cm}$. Assuming the mass of the bicycle plus rider is $75.0 \text{~kg}$, $(b)$ If each complete revolution of the pedals moves the bike $5.10 \text{~m}$ along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses."

A $1.00$-mole sample of ammonia at $14.0 \mathrm{~atm}$ and $25^{\circ} \mathrm{C}$ in a cylinder fitted with a movable piston expands against a constant external pressure of $1.00 \mathrm{~atm}$. At equilibrium, the pressure and volume of the gas are $1.00 \mathrm{~atm}$ and $23.5 \mathrm{~L}$, respectively.
(a) Calculate the final temperature of the sample.
(b) Calculate $q, w$, and $\Delta U$ for the process. The specific heat of ammonia is $0.0258 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}$.

In a hydroelectric power plant, water at $20^{\circ} \mathrm{C}$ is supplied to the turbine at a rate of $0.55 \mathrm{~m}^3 / \mathrm{s}$ through a $200$-m-long, $0.35$-m-diameter cast iron pipe. The elevation difference between the free surface of the reservoir and the turbine discharge is $140 \mathrm{~m}$, and the combined turbine-generator efficiency is $85$ percent. Disregarding the minor losses because of the large length-to-diameter ratio, find the electric power output of this plant.

Imagine that you are the equipment manager of a professional baseball team. One of your jobs is to keep a supply of baseballs for games in your home ballpark. Balls are sometimes lost when players hit them into the stands as either home runs or foul balls. Estimate how many baseballs you have to buy per season in order to make up for such losses. Assume your team plays an 81-game home schedule in a season.

A household refrigerator that has a power input of 450 W and a COP of 1.5 is to cool 5 large watermelons, 10 kg each, to $8^{\circ} \mathrm{C}.$ If the watermelons are initially at $28^{\circ} \mathrm{C},$ determine how long it will take for the refrigerator to cool them. The watermelons can be treated as water whose specific heat is $4.2 \mathrm{kJ} / \mathrm{kg} \cdot^{\circ} \mathrm{C}.$ Is your answer realistic or optimistic? Explain.

A closed-end fund starts the year with a net asset value of 12.00 dollars. By year-end, NAV equals 12.10 dollars. At the beginning of the year, the fund is selling at a 2% premium to NAV. By the end of the year, the fund is selling at a 7 % discount to NAV. The fund paid yearend distributions of income and capital gains of 1.50 dollars.

a. What is the rate of return to an investor in the fund during the year?

b. What would have been the rate of return to an investor who held the same securities as the fund manager during the year?

In a hydroelectric power plant, water at $20^{\circ} \mathrm{C}$ is supplied to the turbine at a rate of $0.6 \mathrm{m}^{3} / \mathrm{s}$ through a 200-m-long, 0.35-m-diameter cast iron pipe. The elevation difference between the free surface of the reservoir and the turbine discharge is 140 m, and the combined turbine–generator efficiency is 80 percent. Disregarding the minor losses because of the large length-to-diameter ratio, determine the electric power output of this plant.