Similarly at B-c interface,

CB

dx

dT

dx

dT

((k

B

>k

C

)

When

dx

dT

constant, T(x) is linear

When

dx

dT

linear, T(x) is quadratic

Hence the correct temperature distribution is

T

x

Two mark

1. A rigid vessel of volume 10m

2

is filled with hydrogen at 35C and 500 kPa. Due to

leakage, some gas has escaped from the vessel until the pressure in the vessel drops

down to 200 kPa, and the corresponding temperature of the gas inside the vessel is found

to be 25C. The amount gas leaked (in kg) from the vessel is___

Ans: 2.291 (range 2.2 to 2.5)

Sol: P

1

=500 kPa

V

1

=10m

3

T

1

= 273+35=308 K

157.4

2

314.8

M

R

R

2

2

H

H

11

1

1

500 10

3.905

4.157 308

PV

m kg

RT

P

2

= 200 kPa (final state)

V

2

= 10m

3

(rigid vessel)

T

2

= 273+25=298K

22

2

2

200 10

1.614

4.157 298

PV

m kg

RT

Amount gas leaked = m

1

–m

2

= 3.905–1.614=2.291kg

2. An air standard diesel engine has a compression ratio of 18 (the ratio of the volume at

the beginning of the compression process to that the end of the compression process),

and a cut off ratio of 3 (the ratio of the volume at the end of the heat addition process to

that at the beginning of the heat addition process). The thermal efficiency (in%) of the

engine is______

Ans: 59 (range 57 to 61)

Sol: r

k

= 18

r

c

= 3

1r

1r

r

1

1

2

y

c

1y

k

th

0.4

1 4.65 1

1

1.4 18 3 1

=0.589=59%