The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of 1000 K is 0.4 . It extracts 150 J of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance 10 . The hot reservoir of the heat pump is at a temperature of 300 K . Which of the following statements is/are correct :
In the given $P-V$ diagram, a monoatomic gas $\left(\gamma=\frac{5}{3}\right)$ is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: $\left(\frac{1}{3}\right)^{0.6} \simeq 0.5, \ln 2 \simeq 0.7$ ].
Which of the following statement(s) is(are) correct?
(Take Stefan-Boltzmann constant = 5.67 $$ \times $$ 10−8 Wm−2K−4 , Wien’s displacement constant = 2.90 $$ \times $$ 10−3 m-K, Planck’s constant = 6.63 $$ \times $$ 10−34 Js, speed of light in vacuum = 3.00 $$ \times $$ 108 ms−1)
(Given, 21.2 = 2.3; 23.2 = 9.2; R is a gas constant)
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