Question 488: Thermodynamics & KTG

Question

A Carnot's engine works as a refrigerator between $$250$$ K and $$300$$ K. It receives $$500$$ cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is :

Accepted Answer

Given,
Cold body temperature (T
2
) = 250 K
Hot body temperature (T
1
) = 300 K
Received heat (Q
2
) = 500 cal
Let, required works done = $$\omega $$
$$	herefore\,\,\,\,$$ For the refrigerator,
Efficiency = $$1 - {{T2} \over {T1}} = {\omega  \over {{Q_2} + \omega }}$$
$$ \Rightarrow $$$$\,\,\,\,$$ 1 $$-$$ $${{250} \over {300}} = {\omega  \over {{Q_2} + \omega }}$$
$$ \Rightarrow $$$$\,\,\,\,$$ $${{{Q_2} + \omega } \over \omega }$$ =  $${{300} \over {50}}$$ = 6
$$ \Rightarrow $$$$\,\,\,\,$$ $$\omega  = {{{Q_2}} \over 5}$$
$$ \Rightarrow $$$$\,\,\,\,$$ $$\omega  = {{500 	imes 4.2} \over 5}$$
$$ \Rightarrow $$$$\,\,\,\,$$ $$\omega  = 420\,J$$

Answer

$$420$$ $$J$$

Answer

$$772$$ $$J$$

Answer

$$2100$$ $$J$$

Answer

$$2520$$ $$J$$

Thermodynamics & KTG

A Carnot's engine works as a refrigerator between $250 K and 300 K. It receives 500$ cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is :

Choose the correct answer: