List of top Thermodynamics Questions on Thermodynamics asked in GATE XE

The temperature of the working fluid in a real heat engine cycle changes during heat addition and heat rejection processes. The maximum and minimum temperatures of the cycle are $T_{\max}$ and $T_{\min}$, respectively. If $\eta_C$ is the thermal efficiency of a Carnot engine operating between these temperature limits, then the thermal efficiency, $\eta$, of the real heat engine satisfies the relation

An insulated rigid tank of volume 10 m$^3$ contains air initially at 1 MPa and 600 K. A valve connected to the tank is opened, and air is allowed to escape until the temperature inside the tank drops to 400 K. The temperature of the discharged air can be approximated as the average of the initial and final temperatures of the air in the tank. Neglect kinetic and potential energies of the discharged air. Assume that air behaves as an ideal gas with constant specific heat so that internal energy $u = c_p T$ and enthalpy $h = c_p T$. Then, the final pressure of the air in the tank is _________ MPa (round off to 2 decimal places). Assume: $c_p = 1.005$ kJ/(kg K), $\gamma = \frac{c_p}{c_v} = 1.4$

Steam enters a steam turbine at 5 MPa and 600°C, and exits as saturated vapor at 50 kPa. Under steady state condition, the turbine loses heat to the surroundings at the rate of 50 kJ per kilogram of steam flowing through the turbine. The ambient temperature is 300 K, and the heat transfer to the surroundings takes place at the outer surface of the turbine at a temperature of 450 K. The irreversibility per unit mass of steam flowing through the turbine is _________ kJ/kg (round off to 2 decimal places).

A heat engine receives heat at 1000 K and rejects heat to environment at 300 K. Its efficiency is half that of a Carnot engine operating between these temperatures. The work output drives a refrigerator removing heat from a cold space at 260 K at 5.2 kW, rejecting heat at 300 K. The refrigerator COP is half of the Carnot refrigerator. Find the rate of heat supplied to the heat engine (kW). Round off to 2 decimals.

A room contains air at 25°C, 100 kPa and 80% relative humidity. Saturation pressure of water vapor at 25°C is 3.1698 kPa. Find the specific humidity (kg water vapor/kg dry air). Round off to 4 decimals.

An insulated rigid container is divided into two parts by a thin partition. One part of the container contains 6 kg of saturated liquid-vapor mixture with a dryness fraction of 0.7 at 0.3 MPa. The other part contains 12 kg of saturated liquid at 0.6 MPa of the same substance. When the partition is removed and the system attains equilibrium, the final specific volume of the mixture is _________ m$^3$/kg (round off to 2 decimal places).

During a steady state air-conditioning process, air enters a heating section at 15°C with 40% relative humidity and leaves at 30°C. Assuming the heating process takes place at 100 kPa, the relative humidity of the air at exit is _________ % (round off to nearest integer). Saturation pressures of water vapor at 15°C and 30°C are 1.7057 kPa and 4.2469 kPa respectively.

Steam enters a steam turbine at 10 MPa and 600°C with a mass flow rate of 16 kg/s. The steam exits the turbine as saturated vapor at 10 kPa. Under steady state condition, the turbine generates 16.2 MW power. If the ambient temperature is 25°C, the rate of entropy generation in the turbine is _________ kW/K (round off to 2 decimal places).

A steam power plant operates on Rankine cycle. There is a 20% reduction in net work output (kJ/kg). Find the percentage increase in specific steam consumption (kg/kJ). (Answer in integer).

A Carnot heat pump extracts heat from the environment at 250 K and supplies 6 kW of heat to a room maintained at temperature $T_H$. The heat pump requires a power input of 1 kW. The temperature of the room $T_H$ is _________ K (round off to nearest integer).

One of the Maxwell equations is expressed as \(\left( \dfrac{\partial s}{\partial v} \right)_{T = \left( \dfrac{\partial p}{\partial T} \right)_{v}\), where \(s\) is the entropy per unit mass, \(v\) is the mass specific volume, \(p\) is the pressure, and \(T\) is the temperature. In this expression, \(s\) is a continuous function of \(T\) and \(v\). Let \(c_v\) be the specific heat capacity at constant volume for a gas. Then, \(\left( \dfrac{\partial c_v}{\partial v} \right)_{T}\) can be written as}

The general relation among the properties $x$, $y$ and $z$ at any state point can be expressed as \[ \left( \frac{\partial x}{\partial y} \right)_z \left( \frac{\partial y}{\partial z} \right)_x \left( \frac{\partial z}{\partial x} \right)_y = -1 . \] If $p$, $T$ and $h$ are continuous functions and \[ c_p = \left( \frac{\partial h}{\partial T} \right)_p , \] and $\mu$ is the Joule–Thomson coefficient, then \[ \left( \frac{\partial h}{\partial p} \right)_T \] is:

An air-conditioning system consists of an insulated rigid mixing chamber designed to supply air at 24 °C to a building. The mixing chamber mixes two air streams: (i) a cold air stream at 10 °C and mass flow rate $\dot{m}_c$ (kg/s), and (ii) a stream of fresh ambient air at 30 °C and mass flow rate $\dot{m}_a$ (kg/s). Assume air to be an ideal gas with constant specific heat ($c_p = 1.005$ kJ/(kg K), $\gamma = c_p/c_v = 1.4$). Neglect change in kinetic and potential energies as compared to change in enthalpy. Under the steady state condition, the ratio of the mass flow rates of the two streams $(\dot{m}_c/\dot{m}_a)$ is:

An ideal gas mixture consists of 80% N$_2$ and 20% O$_2$ on mass basis. If the total pressure is 300 kPa, then the partial pressure of N$_2$ (in kPa) is
(Molecular weights of N$_2$ = 28 kg/kmol and O$_2$ = 32 kg/kmol)

On the basis of the ideal gas equation and van der Waals equation, the temperatures of a gas at pressure 10 MPa and specific volume 0.005 m$^3$/kg would be, respectively
(Assume gas constant $R = 0.3$ kJ/(kg K), $a = 0.18$ m$^6$ kPa/kg$^2$ and $b = 0.0014$ m$^3$/kg)

An ideal Brayton cycle operates between maximum and minimum temperatures of \( T_3 \) and \( T_1 \), respectively. For constant values of \( T_3 \) and \( T_1 \), the pressure ratio \( r_p \) for maximum work output is:

Gas in a cylinder-piston device expands from state 1 $(p_1, V_1, T_1)$ to state 2 $(p_2, V_2, T_2)$. The expansion process is polytropic, i.e., $pV^n = \text{constant}$, $n \neq 1$. Assuming the ideal gas behaviour, the expression for the work done, $W$, by the system is given by:

A 1.2 m$^{3}$ rigid vessel contains 8 kg of saturated liquid–vapor mixture at 150 kPa. The specific enthalpy of this mixture is _________ kJ/kg (round off to 2 decimal places). At 150 kPa:
$v_f = 0.001053$ m$^{3}$/kg,
$v_g = 1.1594$ m$^{3}$/kg
$h_f = 467.13$ kJ/kg,
$h_g = 2693.1$ kJ/kg

A vertical cylinder–piston device contains a fixed mass of gas in equilibrium. Cross-sectional area of the piston is \(A = 0.05\ \text{m}^2\). Gas pressure is 150 kPa. Find the mass of the piston (kg). Assume atmospheric pressure = 100 kPa and g = 9.81\ \text{m/s}^2. Round off to 2 decimals.

The energy equation for a reversible non-flow process can be expressed as \(\delta q = du + p\,dv\), where \(q\) is the heat transfer per unit mass, \(u\) is the internal energy per unit mass, \(p\) is the pressure, and \(v\) is the mass specific volume. This energy equation is not in exact differential form. It can be made exact differential by multiplying with the following integrating factor: (The temperature \(T\) is absolute temperature)

An air standard Diesel cycle consists of four processes: 1-2 (isentropic compression), 2-3 (constant pressure heat addition), 3-4 (isentropic expansion) and 4-1 (constant volume heat rejection). $T_4$ is the temperature attained at the end of isentropic expansion (3-4) before constant volume heat rejection. The constant volume heat rejection process (4-1) is replaced by a constant pressure heat rejection process (4a-1) such that $T_{4a$ is the temperature reached at the end of isentropic expansion (3-4a), and the state point 1 remains the same. Then}