The entropy of any system is given by S = {\alpha ^2}\beta \ln \left[ {{{\mu kR} \over {J{\beta ^2}}} + 3} \right] where $$\alpha$$ and $$\beta$$ are the constants. $$\mu$$, J, k and R are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively. [Take S = {{dQ} \over T}] Choose the incorrect option from the following :

Which of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning.

The correct relation between the degrees of freedom f and the ratio of specific heat $$\gamma$$ is :

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?

For a gas CP $$-$$ CV = R in a state P and CP $$-$$ CV = 1.10 R in a state Q, TP and TQ are the temperatures in two different states P and Q respectively. Then

A monoatomic ideal gas, initially at temperature T1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If l1 and l2 are the lengths of the gas column, before and after the expansion respectively, then the value of {{{T_1}} \over {{T_2}}} will be :

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :

A heat engine has an efficiency of {1 \over 6}. When the temperature of sink is reduced by 62$${}^{\circ }$$C, its efficiency get doubled. The temperature of the source is :

The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure with mean kinetic energy 2 $$\times$$ 10$$-$$9 J per molecules is :

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A $$\to$$ B and C $$\to$$ D are T1 and T2 (T1 > T2) respectively. Choose the correct option out of the following for work done if processes BC and DA are adiabatic.

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27$${}^{\circ }$$ C to 37$${}^{\circ }$$ C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J mol$$-$$1 k$$-$$1]

Two Carnot engines A and B operate in series such that engine A absorbs heat at T1 and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T3. When workdone in both the cases is equal, to value of T is :

An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90W. How long it would take to increase the internal energy by 2.5 $$\times$$ 103 J ?

The rms speeds of the molecules of Hydrogen, Oxygen and Carbon dioxide at the same temperature are VH, VO and VC respectively then :

The temperature of equal masses of three different liquids x, y and z are 10$${}^{\circ }$$C, 20$${}^{\circ }$$C and 30$${}^{\circ }$$C respectively. The temperature of mixture when x is mixed with y is 16$${}^{\circ }$$C and that when y is mixed with z is 26$${}^{\circ }$$C. The temperature of mixture when x and z are mixed will be :

A cylindrical container of volume 4.0 $$\times$$ 10$$-$$3 m3 contains one mole of hydrogen and two moles of carbon dioxide. Assume the temperature of the mixture is 400 K. The pressure of the mixture of gases is : [Take gas constant as 8.3 J mol$$-$$1 K$$-$$1]

A refrigerator consumes an average 35W power to operate between temperature $$-$$10$${}^{\circ }$$C to 25$${}^{\circ }$$C. If there is no loss of energy then how much average heat per second does it transfer?

A balloon carries a total load of 185 kg at normal pressure and temperature of 27$${}^{\circ }$$C. What load will the balloon carry on rising to a height at which the barometric pressure is 45 cm of Hg and the temperature is $$-$$7$${}^{\circ }$$C. Assuming the volume constant?

An ideal gas is expanding such that PT3 = constant. The coefficient of volume expansion of the gas is :

if the rms speed of oxygen molecules at 0$${}^{\circ }$$C is 160 m/s, find the rms speed of hydrogen molecules at 0$${}^{\circ }$$C.