MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Heat Capacity at Constant Volume

An ideal dies...

Question

An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is 95 kPa and $20^{\circ} C$ . If the maximum temperature in the cycle is not to exceed 2200 K. (Take y for air = 1.4 and $c_{p}$ for air = 1.005 kJ/kgK) then the thermal efficiency is given by:

A

67.9%

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

56.9%

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

34.9%

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

63.5%

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D 63.5%

The properties of air at room temperature are

$c_{p} = 1.005 k J / k g K, c_{v} = 0.718 k J / k g K, R = 0.287 k J / k g K a n d γ = 1.4$

$T_{2} = T_{1} {(\frac{V_{1}}{V_{2}})}^{γ - 1} = (293 K) (20)^{0.4} = 971.1 K$

Process 2-3: constant pressure heat addition,

$\frac{P_{3} V_{3}}{T_{s}} = \frac{P_{2} V_{2}}{T_{2}} \Rightarrow \frac{V_{3}}{V_{2}} = \frac{T_{3}}{T_{2}} = \frac{2200 K}{971.1 K} = 2.265$

Process 3-4: isentropic expansion,

$T_{4} = T_{3} {(\frac{V_{3}}{V_{4}})}^{γ - 1} = T_{3} {(\frac{2.265 V_{2}}{V_{4}})}^{γ - 1} = T_{s} {(\frac{2.265}{r})}^{γ - 1}$

$= (2200) {(\frac{2.265}{20})}^{0.4} [∵ V_{4} = V_{1}]$

$= 920.6 K$

$q_{i n} = h_{3} - h_{1} = c_{p} (T_{3} - T_{2}) = (1.005) (2200 - 971.1) = 1235.04 k J / k g$

$q_{o u t} = u_{4} - u_{1} = c_{v} (T_{4} - T_{1}) = (0.718) (920.6 - 293) = 450.6 k J / k g$

$ω_{n e t, o u t} = q_{i n} - q_{o u t} = 1235 - 450.6 = 784.4 k J / k g$

$η_{t h} = \frac{ω_{n e t, o u t}}{q_{i n}} = \frac{784.4 k J / k g}{1235.04 k J / k g} = 63.5 %$

Suggest Corrections

thumbs-up

19

Similar questions

Q. Air enters a compressor at 100 kPa and

30^{\circ} C

in a Brayton cycle. The air pressure after compression is 500 kPa. If the heat added is 623 kJ/kg, the back work ratio for the cycle is____.
(For air,

γ = 1.4 a n d C_{p} = 1.005 k J / k g K

)

Q. A diesel engine is working with a compression ratio of 15 and expansion ratio of 10. The air standard efficiency of the cycle is

(Assume γ for air=1.4)

Q. A four stroke petrol engine has a compression ratio of 10.5, takes air at 90 kPa and

40^{\circ} C

and is repeated 2500 times per minute. Using constant specific heats
(

c_{p} = 1.005 k J / k g K, c_{v} = 0.718 k J / k g K

γ = 1.4

) at room temperature, then the rate of heat input is _____ kW. if the cycle is to produce 900J/cycle.

Q. An air compressor with compression ratio of

5 (r_{p})

is used to compress air having inlet temperature of 300 K. If the temperature of air at exit is 500 K. The change in temperature of air at exit for unit increase in percentage polytropic efficiency is _____ K.

(γ_{a i r} = 1.4)

(Assume constant inlet temperature and pressure ratio).

Q. Bell-coleman cycle is used to cool the space. Air is taken into the compressor at 1 bar and

10^{\circ} C

. It is compressed with pressure ratio equal to 10. The air is then cooled by

200^{\circ} C

. Expansion and compression follow

P V^{\frac{1}{4}} = C

. The COP is if R = 0.287 kJ/kg K,

C_{p} = 1.005 kJ/kg K

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Heat Capacity

CHEMISTRY

Watch in App

explore_more_icon

Explore more

Heat Capacity at Constant Volume

Standard XII Chemistry

Join BYJU'S Learning Program

CrossIcon