Heat and Thermodynamics

A 25 × 10–3 m3 volume cylinder is filled with
1 mol of O2 gas at room temperature (300K).
The molecular diameter of O2, and its root
mean square speed, are found to be 0.3 nm, and
200 m/s, respectively. What is the average
collision rate (p...

A cylinder with fixed capacity of 67.2 lit
contains helium gas at STP. The amount of heat
needed to raise the temperature of the gas by
20°C is : [Given that R = 8.31 J mol–1 K–1]

When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by
\(\Delta\)T. the heat required to produce the same change in temperature, at a constant pressure is :

One mole of ideal gas passes through a process where pressure and volume obey the relation
\(P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]\).
Here P0 and V0 are constants. Calculate the change in the temp...

Two moles of helium are mixed with n moles of hydrogen. If \({{Cp} \over {Cv}} = {3 \over 2}\) for the mixture, then the value of n is :

One mole of an ideal monoatomic gas is taken along the path ABCA as show in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature, \({27^ \circ }C.\) The work done on the gas will be :

A Carnot's engine works as a refrigerator between \(250\) K and \(300\) K. It receives \(500\) cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerator is :

Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to a reservoir at 100 K...

The value closest to the thermal velocity of a Helium atom at room temperature (300 K) in ms-1 is :
[kB =1.4 \(\times\) 10-23 J/K; mHe = 7 \(\times\) 10 -27 kg ]

Two moles of an ideal monatomic gas occupies a volume V at 27oC. The gas expands adiabatically to a
volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

A steel rail of length 5 m and area of cross section 40cm2
is prevented from expanding along its length while the temperature rises
by 10oC. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10−5 K−1 and 2×1011 Nm−2...

N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total k...

For the P-V diagram given for an ideal gas,

out of the following which one correctly represents the T-P diagram ?

A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by \(\Delta\)T. The net change in its length is zero. Let \(\ell\) be the length of the rod, A i...

An engine operates by taking n moles of an ideal gas through the cycle ABCDA shown in figure. The thermal efficiency of the engine is :
(Take Cv = 1.5 R, where R is gas constant)

In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto 150oC. Immediately, it is put into water of volume 150 cc at 27oC kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40oC. The spe...

An ideal gas has molecules with 5 degrees of freedom. The ratio of specific heats at constant pressure (Cp ) and at constant volume (Cv) is :

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm,
filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to
be 75oC. T is given by: (Give...

An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the
bulk modulus of the material of the cube and \(\alpha\) is its coefficient of linear expansion. Suppose we want to
bring the cube t...

CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for hydrogen gas CP – Cv = b for nitrogen gas The correct relation between a and b is

The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 \(\times\) 105 Pa. If Ni
and Nf are the number of molecules in the room
before and after heat...

A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0oC. If the temperature of the wire is increased and the corresponding change in its time period is
plotted against its temperature, t...

200 g water is heated from 40oC to 60oC. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J/kg/K) :

The ratio of work done by an ideal monoatomic gas to the heat supplied to it
in an isobaric process is :

Which of the following shows the correct relationship between the pressure ‘P’ and density \(\rho\) of an ideal gas at constant temperature ?

A Carnot freezer takes heat from water at 0oC inside it and rejects it to the room at a temperature of 27oC. The latent heat of ice is 336×103 J kg−1. If 5 kg of water at 0oC is converted into ice at 0oC by the freezer, then the energy cons...

\('n'\) moles of an ideal gas undergoes a process \(A\) \(\to\) \(B\) as shown in the figure. The maximum temperature of the gas during the process will be :

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity \(C\) remains constant. If during this process the relation of pressure \(P\) and volume \(V\) is given by \(P{V^n} =\) constant, then \(n\) is give...

A pendulum clock loses \(12\) \(s\) a day if the temperature is \({40^ \circ }C\) and gains \(4\) \(s\) a day if the temperature is \({20^ \circ }C.\) The temperature at which the clock will show correct time, and the co-efficient of linear...

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as \({V^q},\) where \(V\) is the volume of the gas. The value of \(q\) is: ...

Consider a spherical shell of radius \(R\) at temperature \(T\). The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume \(u = {U \over V}\, \propto \,{T^4}\) and pressure $$p = {...

A solid body of constant heat capacity \(1\) \(J/{}^ \circ C\) is being heated by keeping it in contact with reservoirs in two ways:
\((i)\) Sequentially keeping in contact with \(2\) reservoirs such that each reservoir
$$\,\,\,\,\,\,\,\,...

One mole of a diatomic ideal gas undergoes a cyclic process \(ABC\) as shown in figure. The process \(BC\) is adiabatic. The temperatures at \(A, B\) and \(C\) are \(400\) \(K\), \(800\) \(K\) and \(600\) \(K\) respectively. Choose the corr...

Three rods of Copper, Brass and Steel are welded together to form a \(Y\) shaped structure. Area of cross - section of each rod \(= 4c{m^2}.\) End of copper rod is maintained at \({100^ \circ }C\) where as ends of brass and steel are kept ...

Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible ? The surface tension is \(T,\) density of liquid i...

The above \(p\)-\(v\) diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

A Carnot engine, whose efficiency is \(40\%\), takes in heat from a source maintained at a temperature of \(500\) \(K.\) It is desired to have an engine of efficiency \(60\% .\) Then, the intake temperature for the same exhaust (sink) temp...

Helium gas goes through a cycle \(ABCD\) (consisting of two isochoric and isobaric lines) as shown in figure efficiency of this cycle is nearly : (Assume the gas to be close to ideal gas)

A wooden wheel of radius \(R\) is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area \(S\) and length \(L.\) \(L\) is slightly less than \(2\pi R.\) To fit the...

\(100g\) of water is heated from \({30^ \circ }C\) to \({50^ \circ }C\). Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is \(4184\) \(J/kg/K\)):

Three perfect gases at absolute temperatures \({T_1},\,{T_2}\) and \({T_3}\) are mixed. The masses of molecules are \({m_1},{m_2}\) and \({m_3}\) and the number of molecules are \({n_1},\) \({n_2}\) and \({n_3}\) respectively. Assuming no l...

A Carnot engine operating between temperatures \({{T_1}}\) and \({{T_2}}\) has efficiency \({1 \over 6}\). When \({T_2}\) is lowered by \(62\) \(K\) its efficiency increases to \({1 \over 3}\). Then \({T_1}\) and \({T_2}\) are, respectively...

A thermally insulated vessel contains an ideal gas of molecular mass \(M\) and ratio of specific heats \(\gamma .\) It is moving with speed \(v\) and it's suddenly brought to rest. Assuming no heat is lost to the surroundings, Its temperatu...

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from \(V\) to \(32\) \(V\), the efficiency of the engine is

Statement - 1: The temperature dependence of resistance is usually given as \(R = {R_0}\left( {1 + \alpha \,\Delta t} \right).\) The resistance of wire changes from \(100\Omega\) to \(150\Omega\) when its temperature is increased from $$...

One \(kg\) of a diatomic gas is at a pressure of \(8 \times {10^4}\,N/{m^2}.\) The density of the gas is \(4kg/{m^3}\). What is the energy of the gas due to its thermal motion ?

Two moles of helium gas are taken over the cycle \(ABCD,\) as shown in the \(P\)-\(T\) diagram.

Assuming the gas to be ideal the work done on the gas in taking it from \(A\) to \(B\) is :

Two moles of helium gas are taken over the cycle \(ABCD,\) as shown in the \(P\)-\(T\) diagram.

The work done on the gas in taking it from \(D\) to \(A\) is :

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature \(\theta\) along the length \(x\) of the bar from its hot end is best described by which of the following figures?