Heat and Thermodynamics

The temperature of the sink of a Carnot's engine is 300 K and the efficiency of the engine is 0.25 . If the temperature of the source of the engine is increased by 100 K , the efficiency of the engine increased by

The number of rotational degrees of freedom of a monatomic molecule is

The emissivity of a perfect black body is increased to 16 times by increasing its temperature. If the initial temperature is $T$, then final temperature of that black body is

The number of rotational degrees of freedom of a diatomic molecule

The slopes of the isothermal and adiabatic \(p-V\) graphs of a gas are by \(S_I\) and \(S_A\) respectively. If the heat capacity ratio of the gas is \(\frac{3}{2}\), then \(\frac{S_I}{S_A}=\)

The work done by a Carnot engine operating between 300 K and 400 K is 400 J. The energy exhausted by the engine is

An iron sphere having diameter \(D\) and mass \(M\) is immersed in hot water so that the temperature of the sphere increases by \(\delta T\). If \(\alpha\) is the coefficient of linear expansion of the iron then the change in the surface ar...

5 g of ice at \(-30^{\circ} \mathrm{C}\) and 20 g of water at \(35^{\circ} \mathrm{C}\) are mixed together in a calorimeter.
The final temperature of the mixture is (Neglect heat capacity of the calorimeter, specific heat capacity of ice $$...

A car engine has a power of 20 kW. The car makes a roundtrip of 1 h. If the thermal efficiency of the engine is \(40 \%\) and the ambient temperature is 300 K . The energy generated by fuel combustion is

A Carnot engine operates between a source and a sink. The efficiency of the engine is \(40 \%\) and the temperature of the sink is \(27^{\circ} \mathrm{C}\). If the efficiency is to be increased to \(50 \%\), then the temperature of the sou...

A sphere of surface area \(4 \mathrm{~m}^2\) at temperature 400 K and having emissivity 0.5 is located in an environment of temperature 200 K. The net rate of energy exchange of the sphere is (Stefan Boltzmann constant, $$\sigma=5.67 \times...

The number of vibrational degree of freedom of a diatomic molecule is

A gas is expanded from an initial state to a final state along a path on a \(p\)-\(V\) diagram. The path consists of (i) an isothermal expansion of work 50 J , (ii) an adiabatic expansion and (iii) an isothermal expansion of work 20 J . If ...

A metal tape is calibrated at \(25^{\circ} \mathrm{C}\). On a cold day when the temperature is \(-15^{\circ} \mathrm{C}\), the percentage error in the measurement of length is
(Coefficient of linear expansion of metal $$=1 \times 10^{-5}{ }...

The temperature of the sink of a Carnot engine is 250 K . In order to increase the efficiency of the Carnot engine from \(25 \%\) to \(50 \%\), the temperature of the sink should be increased by

In non-rigid diatomic molecule with an additional vibrational mode

The pressure of a gas is proportional to

For a monoatomic ideal gas is following the
cyclic process ABCA shown in the U versus p
plot, identify the incorrect option.

Isothermal process is the graph between

If the volume of a block of metal changes by \(0.12 \%\) when heated through \(20^{\circ} \mathrm{C}\), then find its coefficient of linear expansion.

Boiling water is changing into steam. The specific heat of boiling water is

When the temperature of an ideal gas is increased from 27\(^\circ\)C to 127\(^\circ\)C. Calculate the percentage increase in its \(v_{rms}\).

An ideal gas is taken from state-1 to state- 2 through optional path \(A, B, C\) and \(D\) as shown in the \(p\) - \(V\) diagram. Let \(Q, W\) and \(U\) represent the heat supplied, work done and change in internal energy respectively, then...

A diatomic gas is heated at constant
pressure, what fraction of the heat energy is
used to increase the internal energy?

A Carnot engine whose heat sink is at 27\(^\circ\)C
has an efficiency of 40%. By how much
should its source temperature be changed, so
as to increase its efficiency to 60%?

A glass vessel of volume \(V_o\) is completely filled with a liquid and its temperature is raised by \(\Delta T\). What volume of the liquid will flow over, if the coefficient of linear expansion of glass is \(\alpha_g\) and coefficient of ...

A balloon contains 1500 m\(^3\) of He at 27\(\Upsilon\)C and 4 atmospheric pressure, the volume of He at \(-3\Upsilon\)C temperature and 2 atmospheric pressure will be

A cylinder has a piston at temperature of \(30 \Upsilon\)C. There is all round clearance of \(0.08 \mathrm{~mm}\) between the piston and cylinder wall if internal diameter of the cylinder is \(15 \mathrm{~cm}\). What is the temperature at w...

A gas (\(\gamma\) = 1.5 ) is suddenly compressed to
(1/4 )th its initial volume. Then, find the ratio
of its final to initial pressure.

A system is taken from state-A to state-B
along two different paths. The heat absorbed
and work done by the system along these
two paths are Q\(_1\), Q\(_2\) and W\(_1\), W\(_2\) respectively, then

If two rods of length \(L\) and \(2 L\), having coefficients of linear expansion \(\alpha\) and \(2 \alpha\) respectively are connected end-to-end, then find the average coefficient of linear expansion of the composite rod.

In a steady state, the temperature at the end \(A\) and end \(B\) of a \(20 \mathrm{~cm}\) long rod \(A B\) are \(100 \Upsilon\) and \(0^{\circ} \mathrm{C}\). The temperature of a point \(9 \mathrm{~cm}\) from \(A\) is

A vessel has 6 g of oxygen at pressure p and
temperature 400 K. A small hole is made in
it, so that oxygen leaks out. How much
oxygen leaks out if the final pressure is p/2
and temperature is 300 K?

A refrigerator with coefficient of
performance 0.25 releases 250 J of heat to a
hot reservoir. The work done on the working
substance is

Which one of the graphs below best
illustrates the relationship between internal
energy U of an ideal gas and temperature T of
the gas in K?

Which of the following is not a reversible
process?

Match the following.

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Expansion during heating