MASSACHUSETTS INSTITUTE OF TECHNOLOGY

Thermodynamics of Materials

3.00 Fall 2001

W. Craig Carter

Department of Materials Science and Engineering

Massachusetts Institute of Technology

77 Massachusetts Ave.

Cambridge, MA 02139

Problem Set 2: Due Fri. Sept. 21, Before 5PM in 4-047

Exercise 2.1

The second conclusion of Joule's famous paper is:

That the quantity of heat produced by the friction of bodies, whether solid or liquid, is always proportional to the quantity of force extended. That the quantity of heat capable of increasing the temperature of a pound of water (weighed in vacuo, and taken between 55${}^\circ$and 60${}^\circ$F) by 1${}^\circ$F requires for its evolution the expenditure of a mechanical force represented by the fall of 772 lb. through a space of one foot.

Estimate the minimum amount of time it would take a horse to raise a pound of water by one degree F.

Exercise 2.2

Estimate the typical size of a bedroom. Make the approximation that the molar heat capacity of the gas in a typical bedroom is always $3R$. Estimate the average daily food-energy intake of an MIT student. Estimate how long it would take a student to heat such a room to their body temperature if the room is adiabatically enclosed and the student maintains their weight.

Does the answer depend on whether the student exercises?

How much would your time estimate change if the student gains 10 pounds?

Exercise 2.3

From the state function for an ideal gas, derive an expression for a small change, $dn$, of the number of moles in a system in terms of appropriate thermodynamic variables.

Exercise 2.4

Please do the third problem of chapter 1 in Denbigh and answer the following additional question: What is the size of a water droplet at 20${}^\circ$C that has equal amount of work stored in its surface as the ``compression energy'' associated with expanding against a constant atmosphere of 1 atm.