Heat and Thermodynamics

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If \(d Q\) and \(d W\) represent the heat supplied to the system and the work done on the system respectively. Then according...

At 300 K, the rms speed of oxygen molecules is \(\sqrt {{{\alpha + 5} \over \alpha }}\) times to that of its average speed in the gas. Then, the value of \(\alpha\) will be
(used \(\pi = {{22} \over 7}\))

Heat energy of 184 kJ is given to ice of mass 600 g at \(-12^\circ \mathrm{C}\). Specific heat of ice is \(\mathrm{2222.3~J~kg^{-1^\circ}~C^{-1}}\) and latent heat of ice in 336 \(\mathrm{kJ/kg^{-1}}\)
A. Final temperature of system will be...

A Carnot engine with efficiency 50% takes heat from a source at 600 K. In order to increase the efficiency to 70%, keeping the temperature of sink same, the new temperature of the source will be :

The root mean square velocity of molecules of gas is

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two ...

Match List I with List II

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A hole is drilled in a metal sheet. At \(\mathrm{27^\circ C}\), the diameter of hole is 5 cm. When the sheet is heated to \(\mathrm{177^\circ C}\), the change in the diameter of hole is \(\mathrm{d\times10^{-3}}\) cm. The value of d wil...

Given below are two statements :
Statement I : The temperature of a gas is \(-73^\circ\)C. When the gas is heated to \(527^\circ\)C, the root mean square speed of the molecules is doubled.
Statement II : The product of pressure and volume o...

1 g of a liquid is converted to vapour at 3 \(\times\) 10\(^5\) Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm\(^3\) during this phase change, then the increase in internal energy in the process will b...

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; \(\mathrm{T_3 > T_2 > T_1}\) as :

Let \(\gamma_1\) be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and \(\gamma_2\) be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid...

The average kinetic energy of a molecule of the gas is

\(\left(P+\frac{a}{V^{2}}\right)(V-b)=R T\) represents the equation of state of some gases. Where \(P\) is the pressure, \(V\) is the volume, \(T\) is the temperature and \(a, b, R\) are the constants. The physical quantity, which has dimen...

A sample of gas at temperature \(T\) is adiabatically expanded to double its volume. The work done by the gas in the process is \(\left(\mathrm{given}, \gamma=\frac{3}{2}\right)\) :

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point '\(\mathrm{K}\)' is :

A Carnot engine operating between two reservoirs has efficiency \(\frac{1}{3}\). When the temperature of cold reservoir raised by x, its efficiency decreases to \(\frac{1}{6}\). The value of x, if the temperature of hot reservoir is $$99^\c...

A flask contains Hydrogen and Argon in the ratio $2: 1$ by mass. The temperature of the mixture is $30^{\circ} \mathrm{C}$. The ratio of average kinetic energy per molecule of the two gases ( $\mathrm{K}$ argon/K hydrogen) is :

(Given: Ato...

A thermodynamic system is taken through cyclic process. The total work done in the process is :

The rms speed of oxygen molecule in a vessel at particular temperature is \(\left(1+\frac{5}{x}\right)^{\frac{1}{2}} v\), where \(v\) is the average speed of the molecule. The value of \(x\) will be:
\(\left(\right.\) Take $$\left.\pi=\frac...

Two plates \(\mathrm{A}\) and \(\mathrm{B}\) have thermal conductivities \(84 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}\) and \(126 ~\mathrm{Wm}^{-1} \mathrm{~K}^{-1}\) respectively. They have same surface area and same thickness. They are placed ...

The mean free path of molecules of a certain gas at STP is \(1500 \mathrm{~d}\), where \(\mathrm{d}\) is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at \(373 \mathrm{~K}\) ...

The initial pressure and volume of an ideal gas are P\(_0\) and V\(_0\). The final pressure of the gas when the gas is suddenly compressed to volume \(\frac{V_0}{4}\) will be :
(Given \(\gamma\) = ratio of specific heats at constant pressur...

If the r. m.s speed of chlorine molecule is \(490 \mathrm{~m} / \mathrm{s}\) at \(27^{\circ} \mathrm{C}\), the r. m. s speed of argon molecules at the same temperature will be (Atomic mass of argon \(=39.9 \mathrm{u}\), molecular mass of ch...

An engine operating between the boiling and freezing points of water will have
A. efficiency more than 27%.
B. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures.
C. efficiency equal to $$27 \...

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the...

On a temperature scale '\(\mathrm{X}\)', the boiling point of water is \(65^{\circ} \mathrm{X}\) and the freezing point is \(-15^{\circ} \mathrm{X}\). Assume that the \(\mathrm{X}\) scale is linear. The equivalent temperature corresponding ...

\(1 \mathrm{~kg}\) of water at \(100^{\circ} \mathrm{C}\) is converted into steam at \(100^{\circ} \mathrm{C}\) by boiling at atmospheric pressure. The volume of water changes from \(1.00 \times 10^{-3} \mathrm{~m}^{3}\) as a liquid to $$1....

The root mean square speed of molecules of nitrogen gas at \(27^{\circ} \mathrm{C}\) is approximately : (Given mass of a nitrogen molecule \(=4.6 \times 10^{-26} \mathrm{~kg}\) and take Boltzmann constant $$\mathrm{k}_{\mathrm{B}}=1.4 \time...

The Thermodynamic process, in which internal energy of the system remains constant is

Match List I with List II :

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Consider two containers A and B containing monoatomic gases at the same Pressure (P), Volume (V) and Temperature (T). The gas in A is compressed isothermally to \(\frac{1}{8}\) of its original volume while the gas in B is compressed adiabat...

A gas is compressed adiabatically, which one of the following statement is NOT true.

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

A sample of monoatomic gas is taken at initial pressure of 75 kPa. The volume of the gas is then compressed from 1200 cm3 to 150 cm3 adiabatically. In this process, the value of workdone on the gas will be :

The pressure of the gas in a constant volume gas thermometer is 100 cm of mercury when placed in melting ice at 1 atm. When the bulb is placed in a liquid, the pressure becomes 180 cm of mercury. Temperature of the liquid is :
(Given 0$$^\c...

300 cal. of heat is given to a heat engine and it rejects 225 cal. If source temperature is 227\(^\circ\)C, then the temperature of sink will be ______________ \(^\circ\)C.

As per the given figure, two plates A and B of thermal conductivity K and 2 K are joined together to form a compound plate. The thickness of plates are 4.0 cm and 2.5 cm respectively and the area of cross-section is 120 cm2 for each plate. ...

Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same...

In van der Waal equation \(\left[ {P + {a \over {{V^2}}}} \right]\) [V \(-\) b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants \({a \over b}\) is dimensionally equal to :

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0\(^\circ\)C will be :
(Given gas constant R = 8.3 JK\(-\)...

A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in cm3 is :

Starting with the same initial conditions, an ideal gas expands from volume V1 to V2 in three different ways. The work done by the gas is W1 if the process is purely isothermal, W2, if the process is purely adiabatic and W3 if the process i...

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm ? Both the diameters have been measured at room temperature (27\(^\circ\)C).
(Given : coefficient of linear ther...

One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is \(\frac{\alpha^{2}}{4} \mathrm{R} \,\mathrm{J} / \mathrm{mol} \,\mathrm{K}\); then the value of $$\alpha$...

The pressure \(\mathrm{P}_{1}\) and density \(\mathrm{d}_{1}\) of diatomic gas \(\left(\gamma=\frac{7}{5}\right)\) changes suddenly to \(\mathrm{P}_{2}\left(>\mathrm{P}_{1}\right)\) and \(\mathrm{d}_{2}\) respectively during an adiabatic pr...

The root mean square speed of smoke particles of mass \(5 \times 10^{-17} \mathrm{~kg}\) in their Brownian motion in air at NTP is approximately. [Given \(\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}\)]

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the ...

The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _____________ J. (Given R = 8.31 J/mol.K)