List of practice Questions

Mixing two distinct ideal gases results in an increase in entropy primarily because of

If $A = \begin{bmatrix} 1 & 1 & 2 \\ 2 & 5 & 4 \\ 1 & 0 & 5 \end{bmatrix}$, then the determinant of $\left(A^{2026} - 11A^{2025} - 9A^{2023}\right)$ is equal to:}

An Eigen value of the matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ is $1$. An eigen vector corresponding to it is:}

If $z = x^2 y + e^{xy^2}$, then $\left(\frac{\partial^2 z}{\partial x^2} + \frac{\partial^2 z}{\partial x \partial y}\right)$ evaluated at $(1,0)$ is:}

If $f(x) = x^3$, $0 \le x \le 4$, $f(x+4) = f(x)$ $\forall x \in \mathbb{R}$ and the Fourier series of $f(x)$ is $f(x) = \sum_{n=0}^{\infty} \left(a_n \cos \frac{n\pi x}{2} + b_n \sin \frac{n\pi x}{2}\right)$, then $a_0 =$}

The particular integral of $\left(D^4 - D^3 - 9D^2 - 11D - 4\right)y = e^{-x}$, where $D = \frac{d}{dx}$, is:}

Gibbs-Helmholtz equation relates

Chemical potential is

Mixing entropy arises due to

Fundamental equation of state for ideal gas

A heat engine receives 1000 J of heat from a reservoir at 1000 K and rejects 600 J of heat to a sink at 300 K. This engine is

For a van der Waals gas, the internal energy U

The primary mode of heat transfer to the workpiece in a salt bath furnace is

High excess air in a furnace combustion process generally

Fourier's law of heat conduction relates

Steady-state conduction implies

Entropy of a perfect crystal at 0 K is

Boltzmann equation relates

The driving force for heat conduction is called as:

Furnace efficiency is best defined as the ratio of

A Sankey diagram is primarily used to represent

Saturated steam at 100 \(^\circ\)C condenses on the outside of a tube. Cold fluid enters the tube at 20 \(^\circ\)C and exits at 50 \(^\circ\)C. The value of the Log Mean Temperature Difference (in \(^\circ\)C) is:

Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being \(T_1 = 300\) K and \(T_2 = 350\) K. The heat capacity rates of the two fluids are \(C_1 = 1000\) W/K and \(C_2 = 400\) W/K, and the effectiveness of the heat exchanger is 0.5. The actual heat transfer rate is (in kW)

Adding insulation to a cylindrical pipe with a radius smaller than the critical radius of insulation will

A uniform cylinder of radius 10 cm and mass 20 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 5.0 cm from the central longitudinal axis of the cylinder. What is the rotational inertia of the cylinder about the axis of rotation?