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?

The filament of a light bulb has surface area 64 mm² . The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of the eyes of the observer to be circular with radius 3 mm. Then

(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)

A mixture of ideal gas containing 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure P₀, volume V₀, and temperature T₀. If the gas mixture is adiabatically compressed to a volume $${{{V_0}} \over 4}$$, then the correct statement(s) is/are

(Given, 2^1.2 = 2.3; 2^3.2 = 9.2; R is a gas constant)

One mole of a monatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are [R is the gas constant]