Concise Physical Chemistry

c03 JWBS043-Rogers September 13, 2010 11:24 Printer Name: Yet to Come

54 THE THERMODYNAMICS OF SIMPLE SYSTEMS

Problem 3.5

In a Joule experiment, two 20.3-kg weights fell 1.524 m to drive a paddle wheel

immersed in 6.31 kg of water. The experiment was repeated 20 times, after which

the temperature of the water bath was found to have risen by 0.352 K. What is the

mechanical equivalent of heat in J K−^1 according to this experiment?

Problem 3.6

Show thatdwis an inexact differential for one mole of an ideal gas undergoing a

reversible expansion.

Problem 3.7

The definition of the calorie is that amount of heat that is necessary to raise1gof

water 1 K. As it stands, this definition is approximately valid for temperature changes

not too far from room temperature. Use this approximate definition to predict the

final temperature of 200 g of water at 283 K mixed with 450 g of water at 350 K.

Problem 3.8

Show that, for an ideal gas with constantCV,wehave

T 2

T 1

=

(

V 1

V 2

)CR

V

Problem 3.9

From the kinetic theory of gases, we get the expressionU=^32 RTfor the energy of

an ideal monatomic gas. Show thatdUis an exact differential.

Problem 3.10

(a) How much energy is required to heat 1.0 mol of an ideal monatomic gas at

constantVfrom 25.0 to 75.0 K?

(b) What is the heat input if the process is carried out at constant pressure?

Problem 3.11

A 10.0-g piece of iron was heated to 100.0◦C by immersing it in boiling water

and then quickly transferring it to an insulated beaker containing 1000 g of water

at 25◦C. What was the final temperature of the water? The specific heat of iron is

0.449 Jg−^1 K−^1. The specific heat of water is 4.184 Jg−^1 K−^1.