P22.1 (a) or

(b)

P22.2 (1)

(2)

From (2), (3)

Solving (3) and (1) simultaneously,

we have

(a) and

(b) .

P22.8 . Therefore, .

The heat removed each minute is

or, .

Thus, the work done per sec .

P22.13 Isothermal expansion at

Isothermal compression at

Gas absorbs 1 200 J during expansion.

(a)

(b)

P22.22 (a) First, consider the adiabatic process :

so .

Also

or .

Now, consider the isothermal process : .

Next, consider the adiabatic process : .

But, from above. Also considering the isothermal process, .

Hence, which reduces to .

Finally, .

State / P(kPa) / V(L) / T(K)
A
B
C
D / 1 400
875
445
712 / 10.0
16.0
24.0
15.0 / 720
720
549
549

(b) For the isothermal process :

so .

For the adiabatic process :

and .

For the isothermal process :

and .

Finally, for the adiabatic process :

and .

Process / Q(kJ) / W(kJ) / (kJ)
/ +6.58 / –6.58 / 0
/ 0 / –4.98 / –4.98
/ –5.02 / +5.02 / 0
/ 0 / +4.98 / +4.98
ABCDA / +1.56 / –1.56 / 0

The work done by the engine is the negative of the work input. The output work is given by the work column in the table with all signs reversed.

(c) or

or

P22.28 A Carnot refrigerator runs on minimum power.

For it: so .

Solving part (b) first:

(b)

(a)

P22.34 (a), (b) The quantity of gas is

In process AB,

so

Process BC takes us to:

In process CD:

and

For the entire cycle, . The net work is

The tables look like:

State / T(K) / P(kPa) / V() / (J)
A / 293 / 100 / 500 / 125
B / 673 / 1 840 / 62.5 / 287
C / 1 023 / 2 790 / 62.5 / 436
D / 445 / 152 / 500 / 190
A / 293 / 100 / 500 / 125
Process / Q(J) / output W(J) / (J)
AB / 0 / –162 / 162
BC / 149 / 0 / 149
CD / 0 / 246 / –246
DA / –65.0 / 0 / –65.0
ABCDA / 84.3 / 84.3 / 0

(c) The input energy is , the waste is , and .

(d) The efficiency is: .

(e) Let f represent the angular speed of the crankshaft. Then is the frequency at which we obtain work in the amount of 84.3 J/cycle:

P22.62 (a) For the isothermal process AB, the work on the gas is

where we have used
and /
FIG. P22.62

and

(b) Since AB is an isothermal process,

and

For an ideal monatomic gas, and

Also,

so the total energy absorbed by heat is .

(c)

(d) or