Question

An ideal gas used in Carnot engine has adiabatic expansion ratio 32. It’s specific heat ratio
is 1.40. The efficiency of the engine is A) 0.99 B) 0.75 C) 0.5 D) 0.25

Answer 1

Answer:

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Explanation:

The efficiency of cycle is

η=1−

T

1

T

2

For adiabatic process

TV

γ−1

= constant

For diatomic gas γ=

5

7

T

1

V

1

γ−1

=T

2

V

2

γ−1

T

1

=T

2

(

V

1

V

2

)

γ−1

T

1

=T

2

(32)

5

7

−1

=T

2

(2

5

)

2/5

=T

2

×4

T

1

=4T

2

.

η=(1−

4

1

)=

4

3

=0.75

Answer 2

The efficiency of the engine is 0.75.

Explanation:

The efficiency of cycle is,

η=$1-\frac{T_{2}}{T_{1}}$

for adiabatic process,

diatomic gas γ=$\frac{7}{5}$

$T_{1}=T_{2}(\frac{V_{2}}{V_{1}})$ γ-1

$T_{1}=T_{2}(32)^\frac{7}{5} -1$

$=T_{2}(2^{5})^\frac{2}{5}$

$=T_{2}*4$

$T_{1}=4T_{2}$

η=$(1-\frac{1}{4} )$

$=\frac{3}{4}$

$=0.75$