Question 30: Thermodynamics & KTG

Question

A Carnot engine has the same efficiency between 600 K to 300 K and 1600 K to x K, then the value of x is

Accepted Answer

Efficiency of Carnot engine is given by
$$\eta  = 1 - {{{T_2}} \over {{T_1}}}$$
Given, T
1
= 600 K
T
2
= 300 K
T'
1
= 1600 K and T'
2
= x K
Carnot engine has same efficiency between 600 K to 300 K and 1600 K to x K, so
$$\left( {1 - {{{T_2}} \over {{T_1}}}} \right) = \left( {1 - {{T{'_2}} \over {T{'_1}}}} \right)$$
Substituting all the given values in above equation, we get
$$1 - {{300} \over {600}} = 1 - {x \over {1600}}$$
$$1 - {1 \over 2} = 1 - {x \over {1600}}$$
$${x \over {1600}} = 1 - {1 \over 2} = {1 \over 2}$$
$$ \Rightarrow x = {{1600} \over 2} = 800$$ K

Answer

1600 K

Answer

800 K

Answer

819 K

Answer

900 K

Thermodynamics & KTG

A Carnot engine has the same efficiency between 600 K to 300 K and 1600 K to x K, then the value of x is

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