# Working with Temperature and Gas

1. What is the final temperature if 25 mL of milk 3.0 degrees Celsius is mixed with 150 mL of coffee at 95 degrees Celsius? Start by writing the equation that shows conservation of energy. State any assumptions you make.

2. If the temperature is raised sufficiently high, proteins, DNA, and RNA will actually begin to unfold and lose their structure. When this happens, they will cease to function properly. Small proteins typically unfold between 50 & 80 degrees Celsius.

Consider a small protein that unfolds as a 3 state system.

N = the native state

I = a partially folded state that lies 1.8 kJ/mol above N

U = an unfolded state that lies 7.4 kJ/mol above N

a. Draw an energy diagram to scale so that have a feeling for the spacing.

b. Do you expect the population ratios NI/NN and NU/NI to be the same? Why or why not?

c. What fraction of the total protein population is in each of these states at 95 degrees Celsius? You should have sizeable populations in each. Watch your units.

3. A gas consisting of 5 moles of argon is put through the cycle:

A to B : isothermal reversible

B to C : constant pressure

C to A : constant volume

Assume that the argon behaves ideally and answer the questions below. The heat capacities for argon are CV, m = 3R/2 and CP, m = 5R/2 (Use R = 8.314 J/mol K here)

a. Calculate the temperature, volume, and pressure points at A, B, and C given that:

N = 5 mols

PA = 50 atm

VA = 2 L

VB = 10 L

b. Before doing part C, predict the signs of heat, work, and change of internal energy for each of the 3 steps. Explain your choices.

c. Now calculate the heat (J), work (J), and changes in internal energy (J) for each of the 3 steps & the total cycle. Give your final values in Joules.

d. Comment on the signs and values of the totals. Are they what you expected for this cycle? Why?

#### Solution Preview

See attached sheet, I've calculated some with actual values, the others I've given formulas with the numbers.

1. T = 82.7oC

2. A) Point A: P = 50 atm, V = 2L, T = 243.6K

Point B: P = 10 atm, V = 10 L, T = 243. 6K

Point C: P = 10 atm, V = 2L, T = ...

#### Solution Summary

The expert examines working with temperatures and gas.