The pressure $$(\mathrm{P})$$ and temperature ($$\mathrm{T})$$ relationship of an ideal gas obeys the equation $${\mathrm{PT}}^2=$$ constant. The volume expansion coefficient of the gas will be :

Heat is given to an ideal gas in an isothermal process. A. Internal energy of the gas will decrease. B. Internal energy of the gas will increase. C. Internal energy of the gas will not change. D. The gas will do positive work. E. The gas will do negative work. Choose the correct answer from the options given below :

Heat energy of 184 kJ is given to ice of mass 600 g at $$-12^{\circ }\mathrm{C}$$. Specific heat of ice is $$2222.3\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1^{\circ }}{\mathrm{C}}^{-1}$$ and latent heat of ice in 336 $$kJ/k{\mathrm{g}}^{-1}$$ A. Final temperature of system will be 0$${}^{\circ }$$C. B. Final temperature of the system will be greater than 0$${}^{\circ }$$C. C. The final system will have a mixture of ice and water in the ratio of 5 : 1. D. The final system will have a mixture of ice and water in the ratio of 1 : 5. E. The final system will have water only. Choose the correct answer from the options given below :

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})

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. Assertion A: If $$dQ$$ and $$dW$$ represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics $$dQ=dU-dW$$. Reason R: First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the options given below:

Match List I with List II .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; overflow:hidden;padding:10px 5px;word-break:normal;} .tg th{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px; font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;} .tg .tg-c3ow{border-color:inherit;text-align:center;vertical-align:top} .tg .tg-7btt{border-color:inherit;font-weight:bold;text-align:center;vertical-align:top} .tg .tg-0pky{border-color:inherit;text-align:left;vertical-align:top} List I List II A. Isothermal Process I. Work done by the gas decreases internal energy B. Adiabatic Process II. No change in internal energy C. Isochoric Process III. The heat absorbed goes partly to increase internal energy and partly to do work D. Isobaric Process IV. No work is done on or by the gas Choose the correct answer from the options given below :

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 scales is given by :-

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 root mean square velocity of molecules of gas is

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 :

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 rotator, the ratio, $$\frac{{\gamma }_1}{{\gamma }_2}$$ is :

In an Isothermal change, the change in pressure and volume of a gas can be represented for three different temperature; $${\mathrm{T}}_3>{\mathrm{T}}_2>{\mathrm{T}}_1$$ as :

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 be :

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 of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the option given below :

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

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: Atomic Weight of $\mathrm{Ar}=39.9$ )

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 pressure and at constant volume)

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 $$373\mathrm{K}$$ is approximately:

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: $$($$ Take $$\pi =\frac{22}{7})$$

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 $$27\%$$ D. efficiency less than $$27\%$$ Choose the correct answer from the options given below: