Challenge Questions

This month's Challenge Question:

You are driving your car at a speed of 35 mph when all of a sudden you have to stop the car. You push the brakes, the car stops, and your son (a mechanical engineer major), who is sitting in the back sit, tells you: we are really lucky that the engineers who designed the car brakes many years ago, decided to install different types of brake systems, one for the front wheels and one for the rear wheels. You, an electronics engineer, look back at your son and ask him: Why on Earth did the mechanical engineers do such a stupid thing?

Yes, indeed, why are different types of brakes used in the same car?

The Answer will be posted right here on CR4 on August 4th.Can't wait that long? Well, check out these weekly challenges from CR4:

Makeshift Mercury Measurement: CR4 Challenge (06/23/09)

Of Springs and Acid: CR4 Challenge (06/09/09)

Two Pressure Vessels: CR4 Challenge (05/26/09)

Solar View: CR4 Challenge (05/19/09)

This week's Challenge Question:

John is making a homemade mercury thermometer. He has figured out that he needs 10 mL of Mercury but is reluctant to use his only measuring cup and too cheap to buy one for the one time he'll be handling mercury. Instead he plans on measuring out 10 mL of water, pour it into a thin glass test tube, and draw a line to mark the height of the water. Then he'll remove the water, let the test tube dry, and then fill the test tube with mercury to that line. When John ran this idea by his friend Tom, assuring him he was taking all kinds of precautions with regards to temperature and atmospheric pressure, Tom warned that he'll be under the desired 10 mL even with those precautions. Why did Tom believe he'd measured out less than 10 mL of Mercury?

And the answer is...

The problem with the makeshift mercury measurement using the glass test tube is the meniscus. Water has a concave meniscus whereas mercury has a convex meniscus. As you can see in the image below, a concave meniscus is bowed in the middle whereas a convex meniscus is curved upward. The 10 mL water line will be lower than the 10 mL mercury line, meaning John is measuring less than 10 mL

This week's Challenge Question:

Compress a steel spring and put it inside a small sturdy box. As you know, energy is stored within the spring when it is compressed. Now, fill the box with a corrosive acid. What happens to the energy originally stored in the spring after it is totally corroded?

And the answer is...

By compressing the spring, the crystalline structure of the steel get tensioned and acquires a higher chemical potential. When the corrosive acid is added, this extra chemical energy accelerates the reaction speed (so the corrosion time is shorter) and releases thermal energy so the bath is heated.

Welcome to the June edition of Monthly Challenge Question from Specs & Techs by GlobalSpec:

You are fishing on a beautiful lake. There is a 150 lb rock in your boat. It's in the way so you throw it overboard. What happens to the level of the lake?

The Answer will be posted right here on CR4 on July 7th. Can't wait that long? Well, check out these weekly challenges from CR4:

Makeshift Mercury Measurement: CR4 Challenge (06/23/09)

Of Springs and Acid: CR4 Challenge (06/09/09)

Two Pressure Vessels: CR4 Challenge (05/26/09)

Solar View: CR4 Challenge (05/19/09)

This week's Challenge Question:

Two pressure Vessels (A and B) are connected by a pipe with a closed valve somewhere along its length. The vessel A originally contains gas at 27°C. At the same time Vessel B contains a vacuum. At a certain moment, the valve is opened connecting the A and B. What is the maximum temperature reached by that portion of the gas which is in vessel B?

Here are the assumptions to be made:

No gas leaks to or from the system No heat flow occurs to or from the gas (Constant enthalpy system)

The ideal gas law apply

The ratio of the Specific heat at constant pressure and the specific heat at constant volume is constant, with a value of 1.4

It is easy to find the Temperature in B for a specific case. For example If and the valve is left open until then will be 111°C; But what if does not equal , and the valve is closed before equals ?

And the Answer is....

Let suffix 1 denotes the initial condition and suffix 2 the final condition.

Constant mass gives

In terms of the specific heat at constant pressure the enthalpy is given by Therefore, constant enthalpy gives

Adiabatic expansion in vessel A gives

From these three equations we obtain

This is the general equation for the temperature in B as a function of . Experimentation soon shows that rises as falls, and we can conclude that will be a maximum when (i.e. immediately after the valve has opened). Putting into the general equation however, gives the indeterminate result .

Applying l'Hopital's rule gives

Or,

The highest temperature reached by the gas is therefore,

Note that it is independent of the original Pressure and also independent of the vessel volumes.