A calorimeter of water equivalent $20\mathrm{g}$  contains $180\mathrm{g}$ of water at ${25}^{?}\mathrm{C}$ , ' $\mathrm{m}$  ' grams of steam at   ${100}^{?}\mathrm{C}$ is mixed in it till the temperature of the mixture is ${31}^{?}\mathrm{C}$   . The value of

 

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 = ${\alpha }^2\beta \mathcal{l}n\left[\frac{\mu kR}{J{\beta }^2}+3\right]$ 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.   $[TakeS=\frac{dQ}{T}]$

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)

The temperature of 3.00 mol of an ideal diatomic gas in increased by 40.0°C without changing the pressure of the gas. The molecules in the gas rotate but do not oscillate. If the ratio of change in internal energy of the gas to the amount of work done by the gas is   $\frac{x}{10}.$ Then the value of x (round off to the nearest integer) is________.

(Given R = 8.31 J mol^-1K^-1)