Octane gas $\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)$ at $25^{\circ} \mathrm{C}$ is burned steadily with 80 percent excess air at $25^{\circ} \mathrm{C},$ 1 atm, and 40 percent relative humidity. Assuming combustion is complete and the products leave the combustion chamber at 1000 K, determine the heat transfer for this process per unit mass of octane.

A t=10-mm-thick horizontal layer of water has a top surface temperature of $T_{c}=-4^{\circ} \mathrm{C}$ and a bottom surface temperature of $T_{h}=2^{\circ} \mathrm{C}$. Determine the location of the solid–liquid interface at steady state.

You are interested in learning about how many text messages are sent by ninth-grade students at Reseda High School. You select 30 students at random from the ninth graders at Reseda High and ask each one how many text messages they send in a typical day. a. Are these 30 students the population or a sample? b. Before your started, a friend suggested that you collect data from the 30 ninth graders in Mr. Rossman’s physics class. Why is it better to select ninth-grade students at random?

The prom committee has four sites available for the banquet and three sites for the dance. How many arrangements are possible for the banquet and dance?

Sand from beaches near recent Hawaiian lava flows is angular. Most other beaches, such as those on New York's Long Island, are composed of more rounded p articles. How can you account for the difference in the shape of sediment particles in these two places? (1) The ocean temperature is colder at the Hawaii beach. (2) The Long Island sediment is derived from harder rocks. (3) The Hawaii beach has larger waves and more storms. (4) The Long Island sediments have been on the beach longer.

Sketch the graph of the function by hand. Then use a graphing utility to verify the graph. $f(x)=[4 x]$

Factorise:

$$x ^ { 2 } - 7 x - 18$$

b.

$$4 x ^ { 2 } - 49$$

c.

$$2 x ^ { 2 } - 14 x - 60$$

d.

$$5 x ^ { 2 } + 12 x + 4$$

Suppose that a room containing 1200 $$ ft^ $$ of air is free of carbon monoxide. At time t=0 cigarette smoke containing 4% carbon monoxide is introduced at the rate of 0.1 $$ ft^3/min $$ , and the well-circulated mixture is vented from the room at the same rate. Find a formula for the percentage of carbon monoxide in the room at time t.

Determine whether the situation illustrates correlation or causation. Explain your reasoning, including other factors that might be involved. A random sample of students found that owning a cell phone had a negative correlation with riding the bus to school.

An $\mathrm{MgO}$ component must not fail when a tensile stress of 13.5 MPa (1960 psi) is applied. Determine the maximum allowable surface crack length if the surface energy of $\mathrm{MgO}$ is $1.0 \mathrm{~J} / \mathrm{m}^2$.

Propane fuel $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ is burned in a space heater with 50 percent excess air. The fuel and air enter this heater steadily at 1 atm and $17^{\circ} \mathrm{C},$ while the combustion products leave at 1 atm and $97^{\circ} \mathrm{C}.$ Calculate the heat transferred in this heater, in kJ/kmol fuel.

Suppose that P(A | B) = 0.4 and P(B) = 0.5. Determine the following: a. P(A ∩ B) b. P(A' ∩ B)

A 1.5-kg specimen of a 90 wt% Pb–10 wt% Sn alloy is heated to 250 degree C (480 degree F); at this temperature it is entirely an -phase solid solution .The alloy is to be melted to the extent that 50% of the specimen is liquid, the remainder being the phase. This may be accomplished either by heating the alloy or changing its composition while holding the temperature constant.

(a) To what temperature must the specimen be heated?

(b) How much tin must be added to the 1.5-kg specimen at 250 degree C to achieve this state?

Liquid propane $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ enters a combustion chamber at $25^{\circ} \mathrm{C}$ at a rate of 1.2 kg/mm where it is mixed and burned with 150 percent excess air that enters the combustion chamber at $12^{\circ} \mathrm{C}.$ If the combustion is complete and the exit temperature of the combustion gases is 1200 K, determine (a) the mass flow rate of air and (b) the rate of heat transfer from the combustion chamber.