Thermodynamic Process

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

Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 m². It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : (g = 10 m/s²)

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)

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.