List of top Thermodynamics Questions asked in GATE Engineering Sciences

The typical speeds of a tsunami wave in water depths of 10 m, 100 m, and 1000 m, respectively, are ................

An office uses a heat pump to receive 500 kJ/day heat in winter to maintain its temperature at 300 K. The ambient temperature is 280 K. If the COP of the heat pump is 60% of its theoretical maximum value, the ratio of actual work input to the minimum theoretical work input to the heat pump is $____________$ (rounded off to one decimal place).

In a liquid-vapour phase change process, $\left(\dfrac{dP}{dT}\right)_{sat}$ at 100$^\circ$C for saturated water is 3750 Pa/K. If the resulting change in specific volume ($v_g - v_f$) is 1.672 m$^3$/kg, the enthalpy of vaporization ($h_{fg}$) will be $____________$ kJ/kg (in integer).

In an air-conditioning system, air enters at 20$^\circ$C and 30% relative humidity at a steady rate of 30 m$^3$/min in a humidifier and it is conditioned to 25$^\circ$C and 60% relative humidity. Assuming entire process takes place at pressure of 100 kPa, the mass flow rate of steam added to air in the humidifier is $____________$ kg/min (rounded off to three decimal places).

A rigid tank of 2 $m^3$ internal volume contains 5 kg of water as a saturated liquid–vapor mixture at 400 kPa. Half of the mass of the saturated liquid in the tank is drained-off while maintaining constant pressure of 400 kPa. The final quality of the mixture remaining in the tank is $____________$ (rounded off to two decimal places). Given: At 400 kPa: $v_f = 0.001084 \, m^3/kg$, $v_{fg} = 0.46138 \, m^3/kg$, $v_g = 0.46246 \, m^3/kg$.

Consider a spark ignition engine which operates on an ideal air-standard Otto cycle. It uses a fuel which produces 44 MJ/kg of heat in the engine. If the engine requires 40 mg of fuel to produce 1 kJ of work output, then the compression ratio of the Otto cycle is $____________$ (rounded off to two decimal places). For the entire cycle, use $\dfrac{c_p}{c_v} = 1.4$.

A refrigerator operates on an ideal vapor compression cycle between the pressure limits of 140 kPa and 800 kPa. The working fluid is refrigerant R-134a. The refrigerant enters the compressor as saturated vapor at 140 kPa and exits at 800 kPa. It leaves the condenser as a saturated liquid at 800 kPa. The coefficient of performance (COP) of the refrigerator is $____________$ (rounded off to two decimal places).
Given property data for R-134a:
At 140 kPa: $h_f = 27.06 \, kJ/kg, \, h_g = 239.19 \, kJ/kg$
At 800 kPa: $h_f = 95.48 \, kJ/kg, \, h_g = 267.34 \, kJ/kg$
At 800 kPa and 60$^\circ$C: $h = 296.82 \, kJ/kg$

A steam power plant operates on a simple ideal Rankine cycle. The condenser pressure is 10 kPa and the boiler pressure is 5 MPa. The steam enters the turbine at 600$^\circ$C. Mass flow rate of the steam is 50 kg/s. Neglecting the pump work, the net power output of the plant is $____________$ MW (rounded off to one decimal place).

A piston–cylinder device initially contains $1 \, m^3$ of air at $200 \, kPa$ and $25^\circ C$. Air expands at constant pressure while a heater of $250 \, W$ is switched on for 10 minutes. There is a heat loss of $4 \, kJ$. Assuming air as an ideal gas, the final temperature of air is $____________________$ $^\circ C$ (rounded off to one decimal place). Given: $R = 0.287 \, kJ/kgK$, $c_p = 1.005 \, kJ/kgK$.

A $5 \, kg$ metal block ($c_p = 0.5 \, kJ/kgK$) at $373 \, K$ is placed in $10 \, kg$ of water ($c_p = 4.2 \, kJ/kgK$) at $293 \, K$ inside an insulated rigid container. Find entropy change of universe.

Match the following thermodynamic functions/equations with their expressions:

Steam at 2 MPa and 300$^\circ$C steadily enters a nozzle of inlet diameter 20 cm. Steam leaves with a velocity of 300 m/s. The mass flow rate of steam through the nozzle is 10 kg/s. Assume no work interaction and no change in potential energy. If the heat loss from the nozzle per kg of steam is 3 kJ, the exit enthalpy per kg of steam is $__________$ kJ (rounded off to nearest integer). Given: At 2 MPa and 300$^\circ$C, $v = 0.12551 \, m^3/kg, \, h = 3024.2 \, kJ/kg$

The following statements are given: (i) The third law of thermodynamics deals with the entropy of a substance at the absolute zero temperature.
(ii) Entropy of any non-crystalline structure is zero at absolute zero temperature.
(iii) At the absolute zero temperature, the crystal structure has maximum degree of order.
(iv) The thermal energy of the substance at absolute zero temperature is maximum.
The correct option describing these statements is:

Adiabatic bulk modulus of a substance is defined as:

A rigid tank contains $2 \, kg$ of an ideal gas at $500 \, kPa$ and $350 \, K$. A valve is opened and half of the gas is released. Then valve is closed. Final pressure = $300 \, kPa$. Find final temperature $T_2$ (in K).

An insulated rigid closed tank of $2 \, m^3$ contains saturated liquid-vapor mixture of water at $200^\circ C$. Quality of mixture = $0.75$. Find mass of mixture. Data at $200^\circ C$: $v_f = 0.001156 \, m^3/kg$, $v_{fg} = 0.12620 \, m^3/kg$, $v_g = 0.12736 \, m^3/kg$.

Air at 400 K and 200 kPa is heated at constant pressure to 600 K. Assuming internal energy is a function of temperature only, the magnitude of change in internal energy during this process is __________ kJ/kmol (rounded off to one decimal place). Molar specific heat of air at constant volume: \[ \bar{c}_v = a + bT + cT^2 \] where $a = 19.686 \, \text{kJ/kmol-K}$, $b = 0.002 \, \text{kJ/kmol-K}^2$, $c = 0.5 \times 10^{-5} \, \text{kJ/kmol-K}^3$.

A rigid closed tank of volume $2 \, m^3$ contains $0.1 \, m^3$ of saturated liquid water and $1.9 \, m^3$ of saturated water vapor at $100 \, kPa$. Heat is transferred until the final pressure reaches $2 \, MPa$. Find the magnitude of heat transfer. % Data At $100 \, kPa$: $v_f = 0.001043 \, m^3/kg$, $v_g = 1.694 \, m^3/kg$, $u_f = 417.33 \, kJ/kg$, $u_g = 2506.06 \, kJ/kg$ At $2 \, MPa$: $v_f = 0.001177 \, m^3/kg$, $v_g = 0.09963 \, m^3/kg$, $u_f = 906.42 \, kJ/kg$, $u_g = 2600.26 \, kJ/kg$

If an ideal air-standard Otto cycle and an ideal air-standard Diesel cycle operate on the same compression ratio, then the relation between thermal efficiencies ($\eta_{th}$) of the cycles is:

An ideal Diesel cycle has compression ratio $r = 20$ and cut-off ratio $r_c = 1.5$. At the beginning of compression, $P_1 = 100 \, kPa$, $T_1 = 300 \, K$. Use cold-air-standard assumptions with $c_p = 1.005 \, kJ/kgK$, $\gamma = 1.4$. Find the net work output per unit mass.

Which of the following is an extensive property of a system?

A: The number of properties required to fix the state of a system is given by the “state postulate”.
R: The state of a simple compressible system is completely specified by two independent, intensive properties. About the statements A and R applied to a single-phase system,

A tank of volume $V$ contains a homogeneous mixture of two ideal gases, A and B, at temperature $T$ and pressure $P$. The mixture contains $n_A$ moles of gas A and $n_B$ moles of gas B. If $P_A$ and $P_B$ are the partial pressures of gas A and B, respectively, then:

A one-dimensional nanowire has a linear electron density of $10^8 \, electrons \, cm^{-1}$. The Fermi energy of the system is (in eV) ............ (rounded off to two decimal places). Given: \[ \frac{\hbar^2}{2m} = 0.24 \, (eV)^2 \, s^2 \, kg^{-1} \] where $m$ is the electron mass.

A metal has a certain vacancy fraction at a temperature of 600 K. On increasing the temperature to 900 K, the vacancy fraction increases by a factor of $________________$. Given: $R = 8.31 \ \text{J mol}^{-1}\text{K}^{-1}$, $Q = 68 \ \text{kJ mol}^{-1}$