## 5.5 Problem Set

- Definitions to review: temperature, system, radiation, equilibrium, convection, steady-state, reversible, evaporation, heat, work, conduction, thermodynamics, internal energy, The First Law

- True or false

The First Law says that energy is conserved within the system.

The integral \(\int PdV\) gives the work done for all processes.

To calculate the work done in a reversible process one must only know the initial and final states of the system.

Sometimes the First Law is written as \(\Delta U = Q + W\). In this sign convention work is done by the system on the surroundings.

- Calculations

Change to Fahrenheit and Kelvin readings: 46°C, 30°C, 15°C, 0°C, -10°C, -23°C.

Convert to Celsius scale: 50 K, 300 K, 350 K, 72°F.

The range of naturally occurring air temperatures in the continental U.S. is approximately -66°F to 134°F. What is this on the Celsius scale?

At what temperature would a Celsius and a Fahrenheit thermometer read the same?

- In the text work was given as the integral of pressure times the change in volume. Show this is equivalent to the traditional definition where work is equal to a force times a distance.

4.(a) Sometimes the First Law is given as \[\Delta E=\Delta E_k+\Delta E_p+\Delta U\] where \(\Delta E\) is the total energy of the system, \(\Delta E_k\) is the kinetic energy of the system and \(\Delta E_p\) is the potential energy of the system. Consider a 50 meter high waterfall. What is the potential energy of 2 kg of water at the top of the falls with respect to the bottom. What is its kinetic energy if its horizontal velocity is \(2 m s^{-1}\)?

Assume that there is no energy exchanges with the surroundings. Write the First Law.

Just before the water hits the pool at the bottom of the falls what is the change in potential energy. Where has the energy gone assuming-there is no heat exchange between the liquid and the surroundings.

When the water hits the pool what happens if there is no motion in the pool. Calculate the change in temperature that takes place. (Assume that \(4184 J kg^{-1}\) must be added to the system for a 1°C change.)

For an ideal gas assuming reversible processes how would one calculate \(\Delta U\), \(Q\) and \(W\) for an adiabatic, a constant temperature, a constant pressure and a constant volume process.

Thought questions:

Acquaint yourself with the activity times of several different kinds of organisms. From this information, suggest how each organism has become adapted to its thermal environment. Are there specific physiological characteristics that allow it to survive? Are behavioral sequences important? All organisms require a source of energy. How have food and nutrition requirements influenced the thermal niche of each organism? Discuss activity, resting and dormancy on both a daily and seasonal basis.In general if an organism is at a warmer temperature does it grow and reproduce more quickly? What implications might this have for ecology? How might thermodynamics be helpful?