(Thermo) Where'd the Energy Go?

A process involving 30 J of work is done by a closed system on its surroundings. What is the heat transfer (and in what direction), if the internal energy of the system decreases by 50 J. ?

We made a ton of changes so far (listed below)... But were not sure if they'e even been helpful...
So tell us what you think:

Should we KEEP the changes or just CHUCK em?
Tell us what you LIKE or DISLIKE so we know what to keep!

(Changes Made: Single-Topic 2-Week-Series, Heat Focus, Progressive Questions, Deeper Solutions, Hints, Equation-Oriented Problems etc.)

Cesium-137 is one of the most problematic radioactive isotopes found in many nuclear weapon tests and nuclear accidents such as the Chernobyl & Fukushima disasters. Exposure to it increases chances of cancer, while exposure to high concentrations can lead to serious burns, and even death.

The isotope has a rate of radioactive decay described by the function:

where

• y = amount of material left
• k = the decay constant

The site of a nuclear accident has an abnormally high concentration of Cesium-137. If the decay constant for Cesium-137 is 0.023, how much time does it take for some initial amount of Cesium-137 to decay to half its original amount?

RC Car (Electronics)

You've played with RC cars before, but this time you decide to give your favorite childhood toy a little more juice. Instead of the usual 4 AA batteries (6V) you decide to double it (12V) to see it really race!

How much power is your motor now receiving? Also, does your new circuit satisfy the conservation of power?

(Diff Eq) What's My Particular Solution?

For the ordinary differential equation below:

What is the form of its particular part of the solution?

(Original question contributed by Professor Autar Kaw & modified with permission)

(Fluids) Pressure! Diver Down!

Dave the Diver's just bought a new underwater watch to wear on his diving expeditions. On the packaging, the watch company claims that the device can withstand absolute pressures of up to 1.0 MPa.

"Oh really..." he says as the gears turn in his head. He calculates that...

From this calculation, Dave reasons that he can safely dive with his watch to a maximum depth of 102 m.

a) What is the flaw in Dave's reasoning?

b) To what maximum depth can Dave actually dive with his watch? Round to the nearest tenth of a meter.