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Standard VII

Physics

Inter-Conversion of Temperature in Different Scales

A power cycle...

Question

A power cycle is working on Carnot cycle with monoatomic gas that rejects heat to a river at 12°C. If the thermal efficiency of the cycle is 55%; what is the compression ratio?

3.31

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3.49

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3.70

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3.92

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Solution

The correct option is A 3.31
$n_{c a r n o t} = 1 - \frac{T_{m i n}}{T_{m a x}}$

$\Rightarrow 0.55 = 1 - (\frac{12 + 273}{T_{m a x}})$

$T_{m a x} = 633.33 K$

$∴$ Compression ratio is given as

$\frac{v_{1}}{v_{2}} = {(\frac{T_{2}}{T_{1}})}^{1 / γ - 1} = {(\frac{633.33}{285})}^{1 / 1.66 - 1} = 3.31267$

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A power cycle is working on Carnot cycle with monoatomic gas that rejects heat to a river at 12°C. If the thermal efficiency of the cycle is 55%; what is the compression ratio?

The correct option is A 3.31 ncarnot=1−TminTmax ⇒ 0.55=1−(12+273Tmax) Tmax=633.33 K ∴ Compression ratio is given as v1v2=(T2T1)1/γ−1=(633.33285)1/1.66−1=3.31267