Heat and Thermodynamics

Given below are two statements :
Statement I : When \(\mu\) amount of an ideal gas undergoes adiabatic change from state (P1, V1, T1) to state (P2, V2, T2), then work done is \(W = {{\mu R({T_2} - {T_1})} \over {1 - \gamma }}\), where $$\ga...

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. T...

Given below are two statements :
Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature.
Statement II : The rms speed of oxygen molecules in a gas is \(v\). If the temperature is doubled and the ...

A Carnot engine has efficiency of \(50 \%\). If the temperature of sink is reduced by \(40^{\circ} \mathrm{C}\), its efficiency increases by \(30 \%\). The temperature of the source will be:

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _________ J.

A vessel contains \(14 \mathrm{~g}\) of nitrogen gas at a temperature of \(27^{\circ} \mathrm{C}\). The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be :
Take $$\mathrm{R}=8.32 \mathrm{~J} \mat...

In a carnot engine, the temperature of reservoir is 527\(^\circ\)C and that of sink is 200 K. If the work done by the engine when it transfers heat from reservoir to sink is 12000 kJ, the quantity of heat absorbed by the engine from reservo...

A mixture of hydrogen and oxygen has volume 2000 cm3, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:
[Take gas constant R = 8.3 JK\(-\)1mol$...

A diatomic gas (\(\gamma\) = 1.4) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is __________ J.

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is :
(Given : initial temperature of the bullet = 127\(^\circ\)C, Melting point of the bullet = ...

According to kinetic theory of gases,
A. The motion of the gas molecules freezes at 0\(^\circ\)C.
B. The mean free path of gas molecules decreases if the density of molecules is increased.
C. The mean free path of gas molecules increases if...

For a perfect gas, two pressures P1 and P2 are shown in figure. The graph shows :

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is \(1: 4\), then
A. The r.m.s. velocity of gas molecules in two vessels will be the same.
B. The ratio of pressure in the...

Read the following statements :
A. When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.
B. Two bodies \(P\) and \(Q\) having equal surface areas are maintai...

If \(K_{1}\) and \(K_{2}\) are the thermal conductivities, \(L_{1}\) and \(L_{2}\) are the lengths and \(A_{1}\) and \(A_{2}\) are the cross sectional areas of steel and copper rods respectively such that $$\frac{K_{2}}{K_{1}}=9, \frac{A_{1...

Which statements are correct about degrees of freedom ?
(A) A molecule with n degrees of freedom has n\(^{2}\) different ways of storing energy.
(B) Each degree of freedom is associated with \(\frac{1}{2}\) RT average energy per mole.
(C) A...

In \(1^{\text {st }}\) case, Carnot engine operates between temperatures \(300 \mathrm{~K}\) and \(100 \mathrm{~K}\). In \(2^{\text {nd }}\) case, as shown in the figure, a combination of two engines is used. The efficiency of this combinat...

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the...

The efficiency of a Carnot's engine, working between steam point and ice point, will be :

A heat engine operates with the cold reservoir at temperature 324 K. The minimum temperature of the hot reservoir, if the heat engine takes 300 J heat from the hot reservoir and delivers 180 J heat to the cold reservoir per cycle, is _____...

A geyser heats water flowing at a rate of 2.0 kg per minute from 30\(^\circ\)C to 70\(^\circ\)C. If geyser operates on a gas burner, the rate of combustion of fuel will be ___________ g min\(-\)1.
[Heat of combustion = 8 \(\times\) 103 Jg$$...

A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27\(^\circ\)C. The ratio of their average kinetic energy per molecule respectively will be :

A monoatomic gas at pressure \(\mathrm{P}\) and volume \(\mathrm{V}\) is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of \(40 \mathrm{~K}\) at constant pressure. The increase in the internal energy of the gas in this process is :
(Given $$\mathrm{R}=8.3 \,\mathrm{JK}^{-1} \mathrm{~mol...

A gas has \(n\) degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be :

An ice cube of dimensions \(60 \mathrm{~cm} \times 50 \mathrm{~cm} \times 20 \mathrm{~cm}\) is placed in an insulation box of wall thickness \(1 \mathrm{~cm}\). The box keeping the ice cube at \(0^{\circ} \mathrm{C}\) of temperature is brou...

A steam engine intakes 50 g of steam at 100\(^\circ\)C per minute and cools it down to 20\(^\circ\)C. If latent heat of vaporization of steam is 540 cal g\(-\)1, then the heat rejected by the steam engine per minute is __________ \(\times\)...

The relation between root mean square speed (vrms) and most probable sped (vp) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :

When a gas filled in a closed vessel is heated by raising the temperature by 1\(^\circ\)C, its pressure increases by 0.4%. The initial temperature of the gas is ___________ K.

The ratio of specific heats \(\left( {{{{C_P}} \over {{C_V}}}} \right)\) in terms of degree of freedom (f) is given by :

A copper block of mass 5.0 kg is heated to a temperature of 500\(^\circ\)C and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper : 0.39 J g\(-\)1 \(^\circ\)C\(-\)1 and latent heat of f...

A solid metallic cube having total surface area 24 m2 is uniformly heated. If its temperature is increased by 10\(^\circ\)C, calculate the increase in volume of the cube. (Given \(\alpha\) = 5.0 \(\times\) 10\(-\)4 \(^\circ\)C\(-\)1).

A unit scale is to be prepared whose length does not change with temperature and remains \(20 \mathrm{~cm}\), using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way...

Following statements are given :
(A) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
(C) T...

A certain amount of gas of volume \(\mathrm{V}\) at \(27^{\circ} \mathrm{C}\) temperature and pressure \(2 \times 10^{7} \mathrm{Nm}^{-2}\) expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume ...

A block of ice of mass 120 g at temperature 0\(^\circ\)C is put in 300 g of water at 25\(^\circ\)C. The x g of ice melts as the temperature of the water reaches 0\(^\circ\)C. The value of x is _____________.
[Use specific heat capacity of w...

Let \(\eta_{1}\) is the efficiency of an engine at \(T_{1}=447^{\circ} \mathrm{C}\) and \(\mathrm{T}_{2}=147^{\circ} \mathrm{C}\) while \(\eta_{2}\) is the efficiency at \(\mathrm{T}_{1}=947^{\circ} \mathrm{C}\) and $$\mathrm{T}_{2}=47^{\ci...

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is \(\sqrt2\) times the speed of sound, then the value of n will be :

0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127\(^\circ\)C. Th amount of heat required to double the speed of its molecules is ____________ k cal.
Take R = 2 cal mole\(-\)1 K\(-\)1)

Two metallic blocks M1 and M2 of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M2 is K then the thermal conductivity of M1 will be :
[Assume steady state heat conduction]

A Carnot engine whose heat sinks at 27\(^\circ\)C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency?

A monoatomic gas performs a work of \({Q \over {4}}\) where Q is the heat supplied to it. The molar heat capacity of the gas will be ______________ R during this transformation. Where R is the gas constant.

A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms\(-\)1. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail?
[Specific heat capacity of iron = 0...

A Carnot engine takes 5000 kcal of heat from a reservoir at 727\(^\circ\)C and gives heat to a sink at 127\(^\circ\)C. The work done by the engine is

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation \({{dp} \over {dv}} = - ap\). If p = p0 at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is...

A reversible engine has an efficiency of \({1 \over 4}\). If the temperature of the sink is reduced by 58\(^\circ\)C, its efficiency becomes double. Calculate the temperature of the sink :

A sample of gas with \(\gamma\) = 1.5 is taken through an adiabatic process in which the volume is compressed from 1200 cm3 to 300 cm3. If the initial pressure is 200 kPa. The absolute value of the workdone by the gas in the process = _____...

A mixture of hydrogen and oxygen has volume 500 cm3, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-

Two thin metallic spherical shells of radii r1 and r2 (r1 < r2) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $$\theta$...