Thermodynamics practice · Mixed difficulty

Temperature of $100 \mathrm{gm}$ water is changed from $0^{\circ} \mathrm{C}$ to $3^{\circ} \mathrm{C}$ in this process, heat supplied to water will be (specified heat of water $=1 \mathrm{~cal} \mathrm{~g}^{-1}{ }^{\circ} \mathrm{C}^{-1}$

The specific heat of an ideal gas varies with temperature $T$ as

If a system undergoes contraction of volume, then the work done by the system is

(A): $C_p$ is always greater than $C_V$ in gases.
(R): Work done at constant pressure is more than at constant volume.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Efficiency of a reversible heat engine will be highest at $- 273^\circ C$ temperature of cold reservoir.

Reason R: The efficiency of Carnot’s engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as $\eta = \left( {1 - \frac{{{T_2}}}{{{T_1}}}} \right)$.
In the light of the above statements, choose the correct answer from the options given below

A given mass of a gas is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restrored and is pressure is then found to be 0.75 of its initial pressure. The ratio of the specific heats of the gas is approximately

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats 1.4. Vessel is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by ($R$ = Universal gas constant)

A carnot engine, having efficiency of $\eta = \frac{1}{{20}}$ as heat engine, is used as a refrigerator. If the work done on the system is 20 J, the amount of energy absorbed from the reservoir at lower temperature is

A sample of gas expands from volume ${V_1}$to ${V_2}$ . The amount of work done by the gas is maximum when the expansion is

The volume of an ideal diatomic gas is doubled isothermally, the internal energy

The first law of thermodynamics is based on the law of conservation of

In adiabatic process, the work done by system is $50 \mathrm{~J}$, then

A refrigerator consumes an average 35 W 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 bullet of mass $5\,g,$ travelling with a speed of $210\,\,m/s,\,$ strikes a fixed wooden target. One-half of its kinetic
energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of
temperature of the bullet, if the specific heat of its material is $0.030\,\,\,\mathrm{cal }{g^{ - 1}}\,\,^\circ {C^{ - 1}}$ is close to

Which of the following is not a state function?

Assertion: Coefficient of performance in refrigerator may be greater than one.
Reason: Heat extracted from lower temperature reservoir.

A gaseous mixture enclosed in a vessel consists of $3 \mathrm{~g}$ mole of a gas $X$ with $\gamma=(5 / 3)$ and some amount of gas $Y$ with $\gamma=(7 / 5)$ at a temperature $T$. The gases $X$ and $Y$ do not react with each other and are assumed to be ideal. If $\gamma$ for the gaseous mixture is $\left(\frac{29}{23}\right)$, then the number of gram moles of the gas $Y$ is

Universal gas constant is

At $500 \mathrm{~K}$ for an isobaric process.

$\Delta \mathrm{S}_{\text {system }}=-10 \frac{\mathrm{kJ}}{\mathrm{mol} \mathrm{K}} \text { and } \Delta \mathrm{S}_{\text {surr }}=12 \frac{\mathrm{kJ}}{\mathrm{molK}}$

Therefore, $\Delta \mathrm{G}$ for the entire process is-

Statement-1: A quasi-static process is so called because it is a sudden and large change of the system.
Statement-2: An adiabatic process is no quasi-static because it is a sudden and large change of the system.

In an isobaric process, the absolute temperature is doubled. The mean free path $\left( \lambda \right)$ and the relaxation time $\left( \tau \right)$ will become respectively

A balloon filled with helium ($32^\circ C$ and 1.7 atm) bursts. Immediately afterwards; the expansion of helium can be considered as

Heat added to a system is equal to

The temperature of 5 moles of a gas at constant volume is changed from 100$^ \circ C$ to 120$^ \circ C$. The change in internal energy is 80 J. the total heat capacity of the gas at constant volume will be in $\mathrm{J}{\mathrm{K}^{ - 1}}$ is

Statement-1: The quantity of heat in a solid body determines its temperature.
Statement-2: Whenever heat is supplied to a solid body which is not undergoing phase change the temperature of the solid body increases.

One mole of an ideal diatomic gas undergoes a thermodynamic process, in which its molar heat capacity varies directly proportional to temperature as ${C}=\alpha{T}$, where $\alpha$ is a positive constant. Work done by the gas when it is heated from initial temperature $T_0$ to a final temperature $3 T_0$ will be

A bullet of mass $10 \times 10^{-3} \mathrm{~kg}$ moving with a speed of $20 \mathrm{~ms}^{-1}$ hits an ice block $\left(0^{\circ} \mathrm{C}\right)$ of $990 \mathrm{~g}$ kept at rest on a frictionless floor and gets embedded in it. If ice takes $50 \%$ of KE lost by the system, the amount of ice melted (in grams) approximately is: $(J=4.2 \mathrm{~J} / \mathrm{cal}$; latent heat of ice $=80 \mathrm{~cal} / \mathrm{g}$)

A sample of ideal gas $(\gamma=1.4)$ is heated at constant pressure. If an amount $140 \mathrm{~J}$ of heat is supplied to the gas, find (a) the change in internal energy of the gas, (b) the work done by the gas.

The first operation involved in a carnot cycle is

If $C_p$ and $C_v$ are the specific heats for a gas at constant pressure and at constant volume respectively, then the relation $C_p-C_v=R$ is exact for