Thermodynamics problems

In a polytropic process where $pv^n = constant$, what expression represents the heat transfer (Q) in terms of work transfer?

A gas turbine unit has a gas flow of 15 kg/s. The turbine develops 12000 kW of power. The inlet and outlet enthalpies are 1260 kJ/kg and 400 kJ/kg, respectively. The inlet and outlet gas velocities are 50 m/s and 110 m/s, respectively. What is the rate at which heat is rejected from the turbine?

A cyclic heat engine operates between a source at 1000°C and a sink at 40°C. What is the least rate of heat rejection per kW net output of the engine?

In an air standard cycle, the compression ratio is 14. The pressure and temperature at the beginning of compression are 1 bar and 300 K. The temperature after heat addition at constant pressure is 2275 K. Given $C_p = 1.005 \text{ kJ/kg-K}$, $C_v = 0.718 \text{ kJ/kg-K}$, and $R = 0.287 \text{ kJ/kg-K}$, what is the thermal efficiency of the cycle?

A reversible heat engine operates between two reservoirs at temperatures 700°C and 50°C. This engine drives a reversible refrigerator operating between 60°C and -25°C. The heat transfer to the engine is 2500 kJ/kg, and the net work output of the combined plant is 400 kJ/kg. Determine the heat transfer to the refrigerant.

The Clausius inequality states that the cyclic integral of $\frac{\delta Q}{T}$ is always greater than or equal to zero.

It is proposed to construct a new temperature scale (°N) where the ice point is assigned $5°N$ and the steam point is assigned $20°N$. If the pressure of an ideal gas at constant volume is used as the thermometric property, what is the Kelvin absolute zero on this new scale, assuming a linear relationship between pressure and temperature?

The area of the inlet pipe in a gas turbine, taking the specific volume of the gases at the inlet as 0.45 $m^3$/kg and the mass flow rate as 15 kg/s with an inlet velocity of 50 m/s is ____ $m^2$.

Match the thermodynamic concepts with their descriptions:

Which of the following statements accurately describes the concept of thermodynamic work?

What distinguishes intensive and extensive properties in thermodynamics?

Which of the following is a correct statement of the first law of thermodynamics for a cycle?

What is the physical significance of the Helmholtz function?

What does the dryness fraction of steam represent?

Describe the key processes involved in a vapor compression cycle and their representation on a p-h diagram.

The Clausius inequality implies that it is impossible to construct a device that transfers heat from a cold reservoir to a hot reservoir without any work input.

In the context of thermodynamics, what is a 'system'?

Explain the significance of the triple point of a substance.

The zeroth law of thermodynamics states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with ____.

What is the thermodynamic definition of 'exergy'?

Explain the concept of a quasi-static process and its importance in thermodynamics.

What are the limitations of the first law of thermodynamics?

A pure substance can only exist in a single phase at any given temperature and pressure.

What is the physical significance of the Clapeyron equation?

According to the Kelvin-Planck statement, it is impossible for any device to operate in a thermodynamic cycle and produce net work while exchanging heat with only ____.

Match the thermodynamic cycles with their applications:

In thermodynamics, what is meant by 'available energy'?

What is the significance of the T-S diagram in thermodynamic analysis?

Enthalpy is a path function, meaning its value depends on the path taken during a process.

According to the Clausius statement of the second law of thermodynamics, it is impossible to construct a device that operates in a cycle and transfers heat from a colder body to a hotter body without ____.

Which of the following is a correct interpretation of the Maxwell relations?

Describe the concept of continuum in thermodynamics and its limitations.

What is the relationship between internal energy, enthalpy, and flow work?

For an ideal gas undergoing an adiabatic process, the product of pressure and volume remains constant.

The air standard efficiency of an Otto cycle depends primarily on the ____.

Match each law with its correct statement:

In a throttling process, which thermodynamic property remains constant?