Thermodynamics and Chemistry

CHAPTER 3 THE FIRST LAW

PROBLEMS 99

caption. For compression along this path, starting atV D0:3000dm^3 andTD300:0K and

ending atVD0:1000dm^3 , find the final temperature to0:1K and the work.

gas vacuum

TextD300:0K

pD3:00bar

VD0:500m^3

TD300:0K

pD 0

VD1:00m^3

Figure 3.25

3.8 Figure3.25shows the initial state of an apparatus containing an ideal gas. When the stopcock

is opened, gas passes into the evacuated vessel. Thesystemis the gas. Findq,w, andÅU

under the following conditions.

(a)The vessels have adiabatic walls.

(b)The vessels have diathermal walls in thermal contact with a water bath maintained at

300:K, and the final temperature in both vessels isTD300:K.

3.9 Consider a reversible process in which the shaft of system A in Fig.3.10makes one revolution

in the direction of increasing#. Show that the gravitational work of the weight is the same as

the shaft work given bywDmgrÅ#.

Table 3.2 Data for Problem 3. 10. The values are from Joule’s 1850 papera

and have been converted to SI units.

Properties of the paddle wheel apparatus:

combined mass of the two lead weights................ 26:3182kg

mass of water in vessel............................... 6:04118kg

mass of water with same heat capacity

as paddle wheel, vessel, and lidb................... 0:27478kg

Measurements during the experiment:

number of times weights were wound up and released... 20

change of elevation of weights during each descent..... 1:5898m

final downward velocity of weights during descent...... 0:0615m s^1

initial temperature in vessel........................... 288:829K

final temperature in vessel............................ 289:148K

mean air temperature................................ 289:228K

aRef. [ 84 ], p. 67, experiment 5.

bCalculated from the masses and specific heat capacities of the materials.

3.10 This problem guides you through a calculation of the mechanical equivalent of heat using data
from one of James Joule’s experiments with a paddle wheel apparatus (see Sec.3.7.2). The
experimental data are collected in Table3.2.
In each of his experiments, Joule allowed the weights of the apparatus to sink to the floor
twenty times from a height of about1:6m, using a crank to raise the weights before each
descent (see Fig.3.13on page 86 ). The paddle wheel was engaged to the weights through the