A Carnot's cycle operating between T1= 600 K and T2 = 300 K producing 1.5 kJ of mechanical work per cycle. The heat transferred to the engine by the reservoirs is

Question

A Carnot's cycle operating between T1= 600 K and T2 = 300 K producing 1.5 kJ of mechanical work per cycle. The heat transferred to the engine by the reservoirs is (A) 2.5 k J (B) 3 k J (C) 3.5 k J (D) 4 k J

Tardigrade Admin · Accepted Answer

Here, T1 = 600 K, T2= 300 K, W = 1.5k J = 1500 J, As η = 1 -(T2/T1) = 1 -(300/600) = (1/2) Also, η= ( textwork done / textheat supplied) = (W/Q1) ∴ Q1 = (W/η) = (1500/1/2 ) = 3000 J = 3 kJ

Q. A Carnot's cycle operating between $T_{1} = 600 K$ and $T_{2} = 300 K$ producing $1.5 k J$ of mechanical work per cycle. The heat transferred to the engine by the reservoirs is

$2.5 k J$

$3 k J$

$3.5 k J$

$4 k J$

Here, $T_{1} = 600 K,$
$T_{2} = 300 K,$
$W = 1.5 k J = 1500 J,$
As $η = 1 - \frac{T _{2}}{T _{1}} = 1 - \frac{300}{600} = \frac{1}{2}$
Also, $η = \frac{work done}{heat supplied} = \frac{W}{Q _{1}}$
$∴ Q_{1} = \frac{W}{η} = \frac{1500}{1/2}$
$= 3000 J = 3 k J$

Q. A Carnot's cycle operating between T1​=600K and T2​=300K producing 1.5kJ of mechanical work per cycle. The heat transferred to the engine by the reservoirs is

2.5kJ

3kJ

3.5kJ

4kJ