Basic Concepts and Zeroth Law · Thermodynamics · GATE ME

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

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 $$100$$ $$K$$, the change in molar specific enthalpy is _______________ $$J/mol.$$

The internal energy of an ideal gas is a function of

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 and $$R$$ is characteristic gas constant. The $$S{\rm I}$$ unit of a is

The specific heats of an ideal gas depend on its

The definition of 1 K as per the internationally accepted temperature scale is

A body of weight $$100$$ $$N$$ falls freely a vertical distance of $$50m$$.The atmospheric drag force is $$0.5N.$$ For the body, the work interaction is

An insulated rigid vessel contains a mixture of fuel and air. The mixture is ignited by a minute spark. The contents of the vessel experience.

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 kPa, the total volume of the container is 10 m³ and the temperature of the contents of the container is 300 K. If the mass of gas-X in the container is 2 kg, then the mass of gas-Y in the container is ____ kg. (Rounded off to one decimal place)

Assume that the universal gas constant is 8314 J kmol^-1K^-1.

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 fitted to the wall of the vessel is $$0.5$$ bar. If the gas constant of air is
$$R =287J/kgK$$ and the atmospheric pressure is $$1$$ bar, the mass of air (in $$kg$$) in the vessel is

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 higher in the end open to atmosphere). The universal gas constant is $$8314$$ $$J/kmol$$-$$K,$$ atmospheric pressure is $$1.01325$$ bar, acceleration due to gravity is $$9.81$$ $$m/{s^2}$$ and density of mercury is $$13600$$ $$kg/{m^3}.$$ The mass of nitrogen (in $$kg$$) in the vessel is _________

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 $$T{}_2 = 3{T_1}/4.$$ Then, it undergoes a constant volume process $$2$$-$$3$$ such that $${T_3} = {T_1}/2.$$ The ratio of the final volume to the initial volume of the ideal gas is

Match items from groups, $${\rm I},$$ $${\rm II},$$ $${\rm III},$$ $${\rm IV}$$ and $$V$$

A football was inflated to a gauge pressure of $$1$$ bar when the ambient temperature was $${15^ \circ }C$$. When the game started next day, the air temperature at the stadium was $${5^ \circ }C$$.
Assume that the volume of the football remains constant at $$2500c{m^3}$$

The amount of heat lost by the air in the football and the gauge pressure of air in the football at the stadium respectively equal

A football was inflated to a gauge pressure of $$1$$ bar when the ambient temperature was $${15^ \circ }C$$. When the game started next day, the air temperature at the stadium was $${5^ \circ }C$$.
Assume that the volume of the football remains constant at $$2500c{m^3}$$

Gauge pressure of air to which the ball must have been originally inflated so that it would equal $$1$$ bar gauge at the stadium is

An isolated thermodynamic system executes a process. Choose the correct statement $$(s)$$ from the following:

Match List - $${\rm I}$$ with List - $${\rm II}$$

List - $${\rm I}$$
$$A.$$ Cetane number
$$B.$$ Approach and range
$$C.$$ $${\left( {{{\delta T} \over {\delta P}}} \right)_h} \ne 0$$
$$D.$$ $$dh = {c_p}\,\,dT,$$ even when pressure varies

List - $${\rm II}$$
$$1.$$ Ideal gas
$$2.$$ Vander Waals gas
$$3.$$ $$S.\,{\rm I}.$$ engine
$$4.$$ $$C.\,{\rm I}.$$ engine
$$5.$$ Cooling towers
$$6.$$ Heat exchangers