Thermodynamics PYQ — Page 13

A balloon carries a total load of $185\mathrm{kg}$ 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 $45\mathrm{cm}$ of $\mathrm{Hg}$ and the temperature is $-7^{\circ}C.$ Assuming the volume constant?

The amount of heat needed to raise the temperature of $4\mathrm{moles}$ of a rigid diatomic gas from $0^{\circ}C$ to $50^{\circ}C$ when no work is done is$(R$ is the universal gas constant)

An electric appliance supplies $6000J{\mathrm{min}}^{-1}$, heat to the system. If the system delivers a power of $90W$. How long it would take to increase the internal energy by $2.5\times {10}^{3}J$?

For a gas ${C}_{\text{P}}-{C}_{\text{V}}=R$ in a state $P$ and ${C}_{\text{P}}-{C}_{\text{V}}=1.10R$ in a state $Q,{T}_{\text{P}}$ and ${T}_{\text{Q}}$ are the temperatures in two different states $P$ and $Q$, respectively. Then

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: 

The $P-V$ diagram of a diatomic ideal gas system going under cyclic process as shown in figure. The work done during an adiabatic process $CD$ is (use $\gamma =1.4)$ : 

On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

A monoatomic gas of mass $4.0u$ is kept in an insulated container. The container is moving with velocity $30m{s}^{-1}$. If the container is suddenly stopped then a change in temperature of the gas ($R=$gas constant) is $\frac{x}{3R}$. Value of $x$ is,

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where $\gamma$ is the ratio of specific heats):

In an adiabatic process, the density of a diatomic gas becomes $32$$n$ times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is:

A gas mixture consists of $3$ moles of oxygen and $5$ moles of argon at temperature $T$. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of $RT$) of the mixutre is :

Consider a mixture of $n$ moles of helium gas and $2n$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its $\frac{{C}_{P}}{{C}_{V}}$ value will be:

Two moles of an ideal monoatomic gas occupy a volume 2V at temperature 300 K...

Initially a gas of diatomic molecules is contained in a cylinder of volume ${V}_{1}$ at a pressure ${P}_{1}$ and temperature $250K$. Assuming that $25%$ of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature $2000K,$ when contained in a volume $2{V}_{1}$ is given by ${P}_{2}$. The ratio ${P}_{2}/{P}_{1}$ is -

Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? Where, $1\rightarrow 2$ is adiabatic. (Graphs are schematic and are not to scale) 

An engine takes in $5$ moles of air at $20^{\circ}C$ and $1\mathrm{atm}$, and compresses it adiabatically to $1/{10}^{\mathrm{th}}$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be $\mathrm{XkJ}$. The value of $X$ to the nearest integer is:

A thermodynamic cycle $xyzx$ is shown on a $V$ - $T$ diagram.  The $P$ - $V$ diagram that best describes this cycle is: (Diagrams are schematic and not to scale)

Match the $\frac{{\text{C}}_{\text{p}}}{{\text{C}}_{\text{v}}}$ ratio for ideal gases with different type of molecules: <table class="pyq-table"><tbody><tr><td>Molecule Type</td><td>${\text{C}}_{\text{p}}/{\text{C}}_{\text{v}}$</td></tr><tr><td>(A) Monoatomic</td><td>(I) $7/5$</td></tr><tr><td>(B) Diatomic rigid molecules</td><td>(II) $9/7$</td></tr><tr><td>(C) Diatomic non-rigid molecules</td><td>(III) $4/3$</td></tr><tr><td>(D) Triatomic rigid molecules</td><td>(IV) $5/3$</td></tr></tbody></table>

In a dilute gas at pressure $P$ and temperature '$t$', the time between successive collision of a molecule varies with $T$ as :

Match the thermodynamics processes taking place in a system with the correct conditions. In the table : $\Delta Q$is the heat supplied, $\Delta W$ is the work done and $\Delta U$ is change in internal energy of the system. <table class="pyq-table"><tbody><tr><td></td><td>Process</td><td></td><td>Condition</td></tr><tr><td>(I)</td><td>Adiabatic</td><td>(A)</td><td>$\Delta W=0$</td></tr><tr><td>(II)</td><td>Isothermal</td><td>(B)</td><td>$\Delta Q=0$</td></tr><tr><td>(III)</td><td>Isochoric</td><td>(C)</td><td>$\Delta U\neq 0,\Delta W\neq 0,\Delta Q\neq 0$</td></tr><tr><td>(IV)</td><td>Isobaric</td><td>(D)</td><td>$\Delta U=0$</td></tr></tbody></table>

A bakelite beaker has volume capacity of $500\mathrm{cc}$ at $30^{\circ}C$. When it is partially filled with ${V}_{m}$ volume (at $30^{\circ}C$) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If ${\gamma }_{\text{bester }}=6\times {10}^{-6}0^{\circ}{C}^{-1},$ where $\gamma$ is the coefficient of volume expansion, then ${V}_{m}$ (in $\mathrm{cc}$ ) is close to $\ldots$

Molecules of an ideal gas are known to have three translational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of $\gamma =(\frac{{C}_{p}}{{C}_{v}})$ are given, respectively, by

A calorimeter of water equivalent $20g$ contains $180g$ of water at $25^{\circ}C$. $m''$' grams of steam at $100^{\circ}C$ is mixed in it till the temperature of the mixture is $31^{\circ}C$. The value of $m''$ is close to (Latent heat of water$=540\mathrm{cal}{g}^{-1}$, specific heat of water$=1\mathrm{cal}{g}^{-1^{\circ}}{C}^{-1}$)

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true ? (A) the mean free path of the molecules decreases (B) the mean collision time between the molecules decreases. (C) the mean free path remains unchanged. (D) the mean collision time relations unchanged.