Question

A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 5 minutes of operation, the heat rejected by the engine melts 0.0400 kg of ice. During this time, how much work W is performed by the engine?

Answer 1

Answer:

W= 4.89 KJ

Explanation:

Lets take

temperature of hot water T₁ = 100⁰C

T₁ = 373 K

Temperature of cold ice T₂= 0⁰C

T₂ = 273 K

The latent heat of ice LH= 334 KJ

The heat rejected by the engine Q= m .LH

Q₂= 0.04 x 334

Q₂= 13.36 KJ

Heat gain by engine = Q₁

For Carnot engine

$Q_1=\dfrac{T_1}{T_2}Q_2$

$Q_1=\dfrac{373}{273}\times 13.36$

Q₁  = 18.25 KJ

The work W= Q₁  - Q₂

W= 18.25 - 13.36 KJ

W= 4.89 KJ

Answer 2

Answer:

W = 4893.77 J

Explanation:

given,

mass of the ice = 0.04 Kg

time of operation = 5 minutes

Heat delivered  =

  $Q_c = m_c \Delta H_f$

  Δ H_f is latent heat of fusion of ice = 334 x 10³ J/Kg

   $Q_c = 0.04 \times 334 \times 10^3$

  $Q_c = 13360\ J$

Work done

W = Q_H - Q_C

$Q_H= (\dfrac{T_H}{T_C})Q_C$

$W= (\dfrac{T_H}{T_C}-1)Q_C$

$W= (\dfrac{373}{273}-1)\times 13360$

W = 4893.77 J