GATE Mechanical Engineering

The thermal efficiency of an ideal air-standard Otto cycle is 0.5 . The value of specific heat ratio of air is 1.4. The compression ratio of the cycle is _________ (rounded off to...

A thermodynamically closed system contains 1 kg of hydrogen. The system undergoes a reversible polytropic process with polytropic index 1.3. The work output during the process is 4...

A thermal power plant is running with no reheat or regeneration. The specific enthalpy and specific entropy of steam at the turbine inlet are $3344 \mathrm{~kJ} \mathrm{~kg}^{-1}$...

In a psychrometric chart, one axis represents dry-bulb temperature. The axis, that is perpendicular to the dry-bulb temperature axis, represents

A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air...

A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an en...

Which one of the following statements regarding a Rankine cycle is FALSE?

A heat engine extracts heat (𝑄 H ) from a thermal reservoir at a temperature of 1000 K and rejects heat (𝑄 L ) to a thermal reservoir at a temperature of 100 K, while producing w...

Which one of the following statements is FALSE?

Consider a mixture of two ideal gases, X and Y, with molar masses M̅ X = 10 kg/kmol and M̅ Y = 20 kg/kmol, respectively, in a container. The total pressure in the container is 100...

The Clausius inequality holds good for

A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m 3 to a final volume of 2.5 m 3 . The polytropic index is given by n = 1.2. The absolute va...

In Fe-Fe 3 C phase diagram, the eutectoid composition is 0.8 weight % of carbon at 725 ºC. The maximum solubility of carbon in α-ferrite phase is 0.025 weight % of carbon. A steel...

Consider a one-dimensional steady heat conduction process through a solid slab of thickness 0.1 m. The higher temperature side A has a surface temperature of 80 °C, and the heat tr...

In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a low-pressu...

An engine running on an air standard Otto cycle has a displacement volume 250 cm 3 and a clearance volume 35.7 cm 3 . The pressure and temperature at the beginning of the compressi...

Which one of the following is an intensive property of a thermodynamic system?

Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume c v is equal to 750 J-kg -1...

In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to 250 kJ/kg. The...

A rigid tank of volume of 8 m 3 is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacua...

At steady state, 500 kg/s of steam enters a turbine with specific enthalpy equal to 3500 kJ/kg and specific entropy equal to 6.5 kJ-kg -1 K -1 . It expands reversibly in the turbin...

One $$kg$$ of an ideal gas (gas constant $$R=287$$ $$J/kg$$-$$K$$) undergoes an irreversible process from state- $${\rm I}$$ ( $$1$$ bar, $$300$$ $$K$$ ) to state-$$2$$ ( $$2$$ bar...

The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is $$2.87{m^3}$$ and $$300$$ $$K,$$ respectively. The gauge pressure indicated by a manometer fitt...

Water (density $$ = 1000$$ $$kg/{m^3}$$) at ambient temperature flows through a horizontal pipe of uniform cross section at the rate of $$1$$ $$kg/s.$$ If the pressure drop across...

The molar specific heat at constant volume of an ideal gas is equal to $$2.5$$ times the universal gas constant ($$8.314$$ $$J/mol.K$$). When the temperature increases by $$100$$ $...

A heat pump absorbs $$10$$ $$kW$$ of heat from outside environment at $$250$$ $$K$$ while absorbing $$15$$ $$kW$$ of work. It delivers the heat to a room that must be kept warm at...

In the Rankine cycle for a system power plant the turbine entry and exit enthalpies are $$2803$$ $$kJ/kg$$ and $$1800$$ $$kJ/kg$$, respectively. The enthalpies of water at pump ent...

One $$kg$$ of an ideal gas (gas constant, $$R = 400$$ $$J/kg.K;$$ specific heat at constant volume, $${c_v} = 1000\,J/kg.K$$ at $$1$$ bar, and $$300$$ $$K$$ is contained in a seale...

A mass $$m$$ of a perfect gas at pressure $${p_1}$$ and volume $${V_1}$$ undergoes an isothermal process. The final pressure is $${p_2}$$ and volume is $${V_2}.$$ The work done on...

A calorically perfect gas (specific heat at constant pressure $$1000$$$$J/kg.K$$) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine ent...

The internal energy of an ideal gas is a function of

An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript $$1$$) and at the end (subscript $$2$$) of the...

The heat removal rate from a refrigerated space and the power input to the compressor are $$7.2$$ $$kW$$ and $$1.8$$ $$kW$$, respectively. The coefficient of performance $$(COP)$$...

The INCORRECT statement about the characteristics of critical point of a pure substance is that

Which of the following statements are TRUE with respect to heat and work? $$(i)$$ They are boundary phenomena $$(ii)$$ They are exact differentials $$(iii)$$ They are path function...

A reversible cycle receives $$40$$ $$kJ$$ of heat from one heat source at a temperature of $${127^ \circ }C$$ and $$37$$ $$kJ$$ from another heat source at $${97^ \circ }C.$$ The h...

Steam at an initial enthalpy of $$100$$ $$kJ/kg$$ and inlet velocity of $$100$$ $$m/s,$$ enters an insulated horizontal nozzle. It leaves the nozzle at $$200$$ $$m/s.$$ The exit en...

In a steam power plant operating on an ideal Rankine cycle, super-heated steam enters the turbine at $$3$$ $$MPa$$ and $${350^ \circ }C.$$ The condenser pressure is $$75$$ $$kPa.$$...

A piston-cylinder device initially contains $$0.4\,{m^3}$$ of air (to be treated as an ideal gas) at $$100$$ $$kPa$$ and $${80^ \circ }C.$$ The air is now isothermally compressed t...

The INCORRECT statement about regeneration in vapor power cycle is that

Work is done on an adiabatic system due to which its velocity changes from $$10$$ $$m/s$$ to $$20$$ $$m/s,$$ elevation increases by $$20$$ $$m$$ and temperature increases by $$1$$...

Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure, $$20$$ percent of the mass is extracted for process heating and the remain...

Steam enters a turbine at $$30bar,$$ $${300^ \circ }C$$ $$\left( {u = 2750\,\,kJ/kg,\,\,h = 2993\,\,kJ/kg} \right)$$ and exits the turbine as saturated liquid at $$15$$ $$kPa$$ $$\...

The Vander-waals equation of state is $$\left( {p + {a \over {{v^2}}}} \right)\left( {v - b} \right) = RT,$$ where $$p$$ is pressure, $$v$$ is specific volume, $$T$$ is temperature...

A rigid container of volume $$0.5$$ $${m^3}$$ contains $$1.0$$ $$kg$$ of water at $${120^ \circ }C$$ $$\left( {{V_f} = 0.00106\,{m^3}/kg,\,\,{v_g} = 0.8908\,\,{m^3}/kg} \right).$$...

One kg of air ($${R = 287\,\,J/kg}$$-$$K$$) under goes irreversible process between equilibrium state $$1\,\,\left( {{{20}^ \circ }C,\,\,0.9\,\,{m^3}} \right)$$ and equilibrium sta...

Which of the following statements regarding a Rankine cycle with reheating are TRUE ? (i) increase in average temperature of heat addition (ii) reduction in thermal efficiency (iii...

A well insulated rigid container of volume $$1{m^3}$$ contains $$1.0$$ $$kg$$ of an ideal gas $$\left[ {{C_p} =1000\,\,\,J/\left( {kg.K} \right)} \right.$$ and $$\left. {{C_v} = 80...

Temperature of nitrogen in a vessel of volume $$2{m^3}$$ is $$288$$ $$K.$$ $$A$$ $$U$$-tube manometer connected to the vessel shows a reading of $$70$$ $$cm$$ of mercury (level hig...

For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy,

One side of a wall is maintained at $$400K$$ and the other at $$300K.$$ The rate of heat transfer through the wall is $$1000W$$ and the surrounding temperature is $${25^ \circ }C.$...

In a Rankine cycle, the enthalpies at turbine entry and outlet are $$3159$$ $$kJ/kg$$ and $$2187$$ $$kJ/kg$$ respectively. If the specific pump work is $$2$$ $$kJ/kg,$$ the specifi...

The $$COP$$ of a Carnot heat pump operating between $${6^ \circ }C$$ and $${37^ \circ }C$$ is ____________

A Carnot engine $$(CE$$-$$1)$$ works between two temperature reservoirs $$A$$ and $$B,$$ where $${T_A} = 900K$$ and $${T_B} = 500K.$$ A second Carnot engine $$(CE$$-$$2)$$ works be...

$$1.5$$ $$kg$$ of water is in saturated liquid state at $$2$$ bar $$\left( {{v_f} = 0.001061\,\,{m^3}/kg,\,\,{u_f} = 504.0kJ/kg,\,\,{h_f} = 505\,\,kJ/kg} \right).$$ Heat is added i...

A reversible heat engine receives $$2$$ $$kJ$$ of heat from a reservoir at $$1000$$ $$K$$ and a certain amount of heat from a reservoir at $$800$$ $$K$$. It rejects $$1$$ $$kJ$$ of...

Steam with specific enthalpy $$\left( h \right)\,\,3214\,\,kJ/kg$$ enters an adiabatic turbine operating at steady state with a flow rate $$10kg/s.$$ As it expands, at a point wher...

Which one of the following pairs of equations describes an irreversible heat engine?

A reversed Carnot cycle refrigerator maintains a temperature of $$ - {5^ \circ }C.$$ The ambient air temperature is $${35^ \circ }C.$$ The heat gained by the refrigerator at a cont...

Steam at a velocity of $$10$$ $$m/s$$ enters the impulse turbine stage with symmetrical blading having blade angle $${30^ \circ }.$$ The enthalpy drop in the stage is $$100kJ.$$ Th...

The maximum theoretical work obtainable, when a system interacts to equilibrium with a reference environment, is called

A certain amount of an ideal gas is initially at a pressure $${p_1}$$ and temperature $${T_1}$$. First, it undergoes a constant pressure process $$1$$-$$2$$ such that $$T{}_2 = 3{T...

An amount of $$100$$ $$kW$$ of heat is transferred through a wall in steady state. One side of the wall is maintained at $${127^ \circ }C$$ and the other side at $${27^ \circ }C$$....

A source at temperature of $$500K$$ provides $$1000$$ $$kJ$$ of heat. The temperature of environment is $${27^ \circ }C.$$ The maximum useful work (in $$kJ$$) that can be obtained...

A closed system contains $$10$$ $$kg$$ of saturated liquid ammonia at $${10^ \circ }C.$$ Heat addition required to convert the entire liquid into saturated vapour at a constant pre...

In a power plant, water (density $$ = 1000\,\,kg/{m^3}$$ ) is pumped from $$80$$ $$kPa$$ to $$3$$ $$MPa$$. The pump has an isentropic efficiency of $$0.85.$$ Assuming that the temp...

Two identical metal blocks $$L$$ and $$M$$ (specific heat $$=0.4$$ $$kJ/kg.K$$), each having a mass of $$5$$ $$kg,$$ are initially at $$313$$ $$K.$$ A reversible refrigerator extra...

A pure substance at $$8$$ $$MPa$$ and $${400^ \circ }C$$ is having a specific internal energy of $$2864$$ $$kJ/kg$$ and a specific volume of $$0.03432\,{m^3}/kg.$$ Its specific ent...

A cylinder contains $$5\,\,{m^3}$$ of an ideal gas at a pressure of $$1$$ bar. This gas is compressed in a reversible isothermal process till its pressure increases to $$5$$ bar. T...

The pressure, temperature and velocity of air flowing in a pipe are $$5$$ $$bar,$$ $$500$$ $$K$$ and $$50$$ $$m/s,$$ respectively. The specific heats of air at constant pressure an...

Air enters an adiabatic nozzle at $$300$$ $$kPa,$$ $$500$$ $$K$$ with a velocity of $$10$$ $$m/s.$$ It leaves the nozzle at $$100$$ $$kPa$$ with a velocity of $$180$$ $$m/s.$$ The...

An ideal gas of mass $$m$$ and temperature $${T_1}$$ undergoes a reversible isothermal process from an initial pressure $${P_1}$$ to final pressure $$P{}_2.$$ The heat loss during...

Air enters an adiabatic nozzle at $$300$$ $$kPa,$$ $$500$$ $$K$$ with a velocity of $$10$$ $$m/s.$$ It leaves the nozzle at $$100$$ $$kPa$$ with a velocity of $$180$$ $$m/s.$$ The...

Steam enters an adiabatic turbine operating at steady state with an enthalpy of $$3251.0kJ/kg$$ and leaves as a saturated mixture at $$15$$ $$kPa$$ with quality (dryness fraction )...

In an experimental set-up, air flows between two stations $$P$$ and $$Q$$ adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at $$P$...

A pump handling a liquid raises its pressure from $$1$$ bar to $$30$$ $$bar.$$ Take the density of the liquid as $$990$$ $$kg/{m^3}$$. The isentropic specific work done by the pump...

The values of enthalpy of steam at the inlet and outlet of a steam turbine in a Rankine cycle are $$2800$$ $$kJ/kg$$ and $$1800$$ $$kJ/kg$$ respectively. Neglecting pump work, the...

The contents of a well-insulated tank are heated by a resistor of $$23\Omega $$ in which $$10A$$ current is flowing. Consider the tank along with its contents as a thermodynamic sy...

Heat and work are

In an experimental set-up, air flows between two stations $$P$$ and $$Q$$ adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at $$P$...