Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.Reason (R) : In isothermal process, PV = constant, while in adiabatic process $P{V}^{\gamma }$ = constant. Here $\gamma$ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas.In the light of the above statements, choose the correct answer from the options given below:

A cup of coffee cools from 90°C to 80°C in t minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is:

A poly-atomic molecule $(C_V=3R,C_P=4R$, where $R$ is gas constant) goes from phase space point $\mathrm{A}\left({\mathrm{P}}_{\mathrm{A}}=10^5\mathrm{Pa},{\mathrm{V}}_{\mathrm{A}}=4\times 10^{-6}{\mathrm{m}}^3\right)$ to point $\mathrm{B}\left({\mathrm{P}}_{\mathrm{B}}=5\times 10^4\mathrm{Pa},{\mathrm{V}}_{\mathrm{B}}=6\times 10^{-6}{\mathrm{m}}^3\right)$ to point $\mathrm{C}({\mathrm{P}}_{\mathrm{C}}=10^4$ $\mathrm{Pa},{\mathrm{V}}_C=8\times 10^{-6}{\mathrm{m}}^3$ ). A to $B$ is an adiabatic path and $B$ to $C$ is an isothermal path. The net heat absorbed per unit mole by the system is :

The work done in an adiabatic change in an ideal gas depends upon only :

Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

An amount of ice of mass $10^{-3}\mathrm{kg}$ and temperature $-10^{\circ }\mathrm{C}$ is transformed to vapour of temperature $110^{\circ }\mathrm{C}$ by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice $=2100{\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$, specific heat of water $=4180{\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$, specific heat of steam $=1920{\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$, Latent heat of ice $=3.35\times 10^5{\mathrm{Jkg}}^{-1}$ and Latent heat of steam $=2.25\times 10^6$ ${\mathrm{Jkg}}^{-1}$ )

Given are statements for certain thermodynamic variables, (A) Internal energy, volume $(\mathrm{V})$ and mass $(\mathrm{M})$ are extensive variables. (B) Pressure (P), temperature ( T ) and density ( $\rho$ ) are intensive variables. (C) Volume (V), temperature (T) and density ( $\rho$ ) are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the options given below :

For a diatomic gas, if ${\gamma }_1=\left(\frac{Cp}{Cv}\right)$ for rigid molecules and ${\gamma }_2=\left(\frac{Cp}{Cv}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct? (Cp and Cv are specific heats of the gas at constant pressure and volume)

The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$, then the ratio of r.m.s. velocities will be :

The kinetic energy of translation of the molecules in 50 g of ${\text{CO}}_2$ gas at 17°C is :

Match the 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) Pressure varies inversely with volume of an ideal gas. (I) Adiabatic process (B) Heat absorbed goes partly to increase internal energy and partly to do work. (II) Isochoric process (C) Heat is neither absorbed nor released by a system. (III) Isothermal process (D) No work is done on or by a gas. (IV) Isobaric process Choose the correct answer from the options given below:

A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is _______ grams. (Latent heat of fusion of lead $=2.5\times 10^4{\mathrm{JKg}}^{-1}$ and specific heat capacity of lead $=125{\mathrm{JKg}}^{-1}$ ${\mathrm{K}}^{-1})$

Water of mass $m$ gram is slowly heated to increase the temperature from $T_1$ to $T_{\gamma }$. The change in entropy of the water, given specific heat of water is $1{\mathrm{Jkg}}^{-1}{\mathrm{K}}^{-1}$, is :

Using the given $P-V$ diagram, the work done by an ideal gas along the path $A B C D$ is :

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature. A. The work done by gas during the process is zero. B. The heat added to gas is different from change in its internal energy. C. The volume of the gas is increased. D. The internal energy of the gas is increased. E. The process is isochoric (constant volume process) Choose the correct answer from the options given below:

The temperature of a body in air falls from $40^{\circ }\mathrm{C}$ to $24^{\circ }\mathrm{C}$ in 4 minutes. The temperature of the air is $16^{\circ }\mathrm{C}$. The temperature of the body in the next 4 minutes will be :

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases. Reason (R) : Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below :

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?