Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Q 5.82 (page 208)

Use the result of the previous problem to calculate the freezing temperature of seawater.

Short Answer

Expert verified

Therefore, the freezing temperature of seawater is-2.167°C

Step by step solution

01

Given information

From the previous problem we have:

T-T0=-NBkT02L

02

Explanation

from the previous problem, we have

T-T0=-NBkT02L

but,NBk=nBRr, so

T-T0=-nBRT02L

Where,

Tois the freezing temperature of water

nBis the number of moles of salt

Lis the fusion latent energy of water and is given as L=333.7×103J

03

Calculations

We have 35 grammes of salt in one kilogram of water because sea water contains calcium and sodium, which have an average molar mass of 30 g/mol, hence in 35g the number of moles are

nB=35g30g/mol=1.167mol

Substitute the values,

role="math" localid="1647204325114" T-T0=-(1.167mol)(8.314J/mol·K)(273K)2333.7×103J=-2.167KT=273K-2.167K=270.833KT=-2.167°C

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Consider an ideal mixture of just 100 molecules, varying in com- position from pure A to pure B. Use a computer to calculate the mixing entropy as a function of NA, and plot this function (in units of k). Suppose you start with all A and then convert one molecule to type B; by how much does the entropy increase? By how much does the entropy increase when you convert a second molecule, and then a third, from A to B? Discuss.

Let the system be one mole of argon gas at room temperature and atmospheric pressure. Compute the total energy (kinetic only, neglecting atomic rest energies), entropy, enthalpy, Helmholtz free energy, and Gibbs free energy. Express all answers in SI units.

The partial-derivative relations derived in Problems 1.46,3.33, and 5.12, plus a bit more partial-derivative trickery, can be used to derive a completely general relation between CPandCV.

(a) With the heat capacity expressions from Problem 3.33 in mind, first considerSto be a function of TandV.Expand dSin terms of the partial derivatives (∂S/∂T)Vand (∂S/∂V)T. Note that one of these derivatives is related toCV

(b) To bring in CP, considerlocalid="1648430264419" Vto be a function ofTand P and expand dV in terms of partial derivatives in a similar way. Plug this expression for dV into the result of part (a), then set dP=0and note that you have derived a nontrivial expression for (∂S/∂T)P. This derivative is related to CP, so you now have a formula for the difference CP-CV

(c) Write the remaining partial derivatives in terms of measurable quantities using a Maxwell relation and the result of Problem 1.46. Your final result should be

CP=CV+TVβ2κT

(d) Check that this formula gives the correct value of CP-CVfor an ideal gas.

(e) Use this formula to argue that CPcannot be less than CV.

(f) Use the data in Problem 1.46 to evaluateCP-CVfor water and for mercury at room temperature. By what percentage do the two heat capacities differ?

(g) Figure 1.14 shows measured values of CPfor three elemental solids, compared to predicted values of CV. It turns out that a graph of βvs.T for a solid has same general appearance as a graph of heat capacity. Use this fact to explain why CPand CVagree at low temperatures but diverge in the way they do at higher temperatures.

Suppose that a hydrogen fuel cell, as described in the text, is to be operated at 75°Cand atmospheric pressure. We wish to estimate the maximum electrical work done by the cell, using only the room temperature data at the back of this book. It is convenient to first establish a zero-point for each of the three substances, H2,O2,andH2O. Let us take Gfor both H2andO2to be zero at 25°C, so that G for a mole of H2Ois -237KJat 25°C.

(a) Using these conventions, estimate the Gibbs free energy of a mole of H2at 75°C. Repeat for O2andH2O.

(b) Using the results of part (a), calculate the maximum electrical work done by the cell at 75°C, for one mole of hydrogen fuel. Compare to the ideal performance of the cell at25°C.

The compression factor of a fluid is defined as the ratio PV/NkT; the deviation of this quantity from 1 is a measure of how much the fluid differs from an ideal gas. Calculate the compression factor of a Van der Waals fluid at the critical point, and note that the value is independent of a and b. (Experimental values of compression factors at the critical point are generally lower than the Van der Waals prediction, for instance, 0.227 for H22O, 0.274 for CO22, and 0.305 for He.)
See all solutions

Recommended explanations on Physics Textbooks

Conservation of Energy and Momentum

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Thermodynamics

Read Explanation

Dynamics

Read Explanation

Magnetism

Read Explanation

Geometrical and Physical Optics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free