Interpretation:
Equation 2.44 is to be derived from the previous step.
Concept introduction:
Heat capacity (thermal capacity) is the quantity of heat required to raise the temperature of the system from the lower limit to higher divided by the temperature difference of the system. When the mass of the system is taken as 1gram, the heat capacity is denoted as specific heat capacity. Similarly, when the mass of the system taken as 1 mole, the heat capacity is referred as molar heat capacity. Heat capacity is generally described as the symbol C. Mathematically, the heat capacity of the system between two temperature T1 and T2 can be expressed as
C (T2, T1) = q / (T2 – T1)
Intriguingly, the molar heat capacities of gaseous systems are determined at constant volume and can be expressed as
Cv = (δU/δT) v
Answer to Problem 2.59E
The derived expression relating molar capacity at constant volume (Cv) of a system with change in volume (Vf and Vi) and change in temperature (Tf and Ti) is given as;
- R ln (Vf/Vi) = Cv ln (Tf/Ti) (or) R ln (Vi/Vf) = Cv ln (Tf/Ti)
Explanation of Solution
In an adiabatic process, the change in work can be expressed in relationship with change in temperature and change in volume.
on comparing equation (1) and (2) we get the following expression,
Moreover, for an adiabatic process Pex = P int and for an ideal gas PV = nRT; the equation (3) can be changed to,
On rearrangement of equation (4), we get
Thus, integrating the equation (5), we get;
Thus,
On changing the sign of the equation 6, we get the expression relating heat capacity at constant volume and volume and temperature change as,
or equation 2.44
Thus, equation 2.44 is derived from the previous steps.
Want to see more full solutions like this?
Chapter 2 Solutions
Physical Chemistry
- I see the same question is answered but the part where it says " That is, Equation 2" I am still confused by the answers the other questions gave. I would like more explanationarrow_forwardCan you rewrite question 6, again this is practice so can you rewrite the steps again! Thank you. (I can't understand or where you got the units from)arrow_forwardPlease explain how to use Boltzmann equation for these problems.arrow_forward
- Evaluate (U/V)T for an ideal gas. Use the expression from Example 4.11. Does your answer make sense?arrow_forward6.21. What assumption is used in the integration of equation 6.11 to get equation 6.12?arrow_forwardDifference between the system and the surroundings. Give examples of both.arrow_forward
- Suppose you have a box with red chairs and another with blue tables, both are made of smaller lego bricks. You pour the content of both boxes into a larger box and shake the box. You notice that, in the end: 1) Red and blue pieces became more evenly distributed throughout the box. II) Many chairs and tables had pieces of them break off. III) Sometimes, pieces stuck to each other forming all sorts of shapes, some containing both red and blue pieces. Are the changes described in items (I), (II) and (III), best compared to changes in entropy, enthalpy, or both? (1) Entropy only; (II) Entropy only; (III) Entropy only (1) Entropy only; (II) Enthalpy only; (III) Entropy only (1) Entropy only; (II) Both; (III) Both (1) Both; (II) Both; (III) Both (1) Entropy only; (II) Enthalpy only; (III) Enthalpy onlyarrow_forwardNeed justification for all statementsarrow_forwardCompare your estimate and to the value obtained from the figure, what do you conclude about the equation you used for your estimate.arrow_forward
- :Carnot heat engine is a . .A Real machine .B Experimental machine .C .Hypothetical machinearrow_forwardUse the necessary constant in solving this problem. See second photo.arrow_forwardExplain how Matthiessen’s rule is convenient in analyzing the experimental data of potassium below 20 K.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Chemistry: Matter and ChangeChemistryISBN:9780078746376Author:Dinah Zike, Laurel Dingrando, Nicholas Hainen, Cheryl WistromPublisher:Glencoe/McGraw-Hill School Pub CoWorld of ChemistryChemistryISBN:9780618562763Author:Steven S. ZumdahlPublisher:Houghton Mifflin College Div