An ideal gas heat engine operates in a Carnot cycle between 127° C and 227° C . It absorbs 6kcal at the higher temperature. The amount of heat (in kcal ) converted into work is equal to

Question

An ideal gas heat engine operates in a Carnot cycle between 127° C and 227° C . It absorbs 6kcal at the higher temperature. The amount of heat (in kcal ) converted into work is equal to (A) 3.5 (B) 1.6 (C) 1.2 (D) 4.8

Tardigrade Admin · Accepted Answer

Efficiency of a carnot engine is given by η=1-(T2/T1) or (W/Q)=1-(T2/T1)⇒ (W/6)=1-((. 273 + 127 .)/(. 273 + 227 .)) ⇒ W=1.2kcal

Q. An ideal gas heat engine operates in a Carnot cycle between $12 7^{\circ} C$ and $22 7^{\circ} C$ . It absorbs $6 k c a l$ at the higher temperature. The amount of heat (in $k c a l$ ) converted into work is equal to

$3.5$

$1.6$

$1.2$

$4.8$

Efficiency of a carnot engine is given by $η = 1 - \frac{T _{2}}{T _{1}}$
or $\frac{W}{Q} = 1 - \frac{T _{2}}{T _{1}} \Rightarrow \frac{W}{6} = 1 - \frac{( 273 + 127 )}{( 273 + 227 )}$
$\Rightarrow W = 1.2 k c a l$

Q. An ideal gas heat engine operates in a Carnot cycle between 127∘C and 227∘C . It absorbs 6kcal at the higher temperature. The amount of heat (in kcal ) converted into work is equal to

3.5

1.6

1.2

4.8