A heat engine operates between a cold reservoir at temperature T₂ = 400K and a hot reservoir at temperature T₁. It takes 300J of heat from the hot reservoir and delivers 240J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be________K.

Match List I with List II.               

List I                                                                                  List II

(a) Isothermal                                                                 (i) Pressure constant

(b) Isochoric                                                                    (ii) Temperature constant

(c) Adiabatic                                                                   (iii) Volume constant

(d) Isobaric                                                                      (iv) Heat content is constant

Choose the correct answer from the options given below:

The entropy of any system is given by S = ${\alpha }^2\beta \mathcal{l}n\left[\frac{\mu kR}{J{\beta }^2}+3\right]$ <!-- [if gte mso 9]><xml> </xml><![endif]--> Where a and b are the constants. $\mu$ , J, k and R no. of moles, mechanical equivalent of heat, Bolzmann constant and gas constant respectively. <!-- [if gte mso 9]><xml> </xml><![endif]-->  $[TakeS=\frac{dQ}{T}]$

Choose the incorrect option from the following:

In the reported figure, hear energy absorbed by a system in going through a cyclic process is_______ pJ.

The amount of heat needed to raise the temperature of 4 moles of a rigid diatomic gas from 0°C to 50°C when no work is done is___________.  (R is the universal gas constant)