M.C.Q (1 Marks)

MCQ 511 Mark

For isothermal expansion of an ideal gas:

A
$\Delta\text{U}=+\text{ve}$
B
$\Delta\text{Q}=+\text{ve}$
C
$\Delta\text{W}=+\text{ve}$
✓
Both $(b)$ and $(c).$

Answer

Correct option: D.

Both $(b)$ and $(c).$

For isothermal expansion,
$\Delta\text{U}=0$
$\Rightarrow\Delta\text{U}=\Delta\text{W}$
Here, $\Delta\text{W}\rightarrow+\text{ve}$
$\Rightarrow\Delta\text{Q}\rightarrow+\text{ve}$

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MCQ 521 Mark

Mechanical equivalent of heat is equal to the amount of:

A
Work done to produce $1 \text{cal}$ heat.
B
A conversion factor between calorie and joule.
✓
Both $(a)$ and $(b).$
D
Neither $(a)$ nor $(b).$

Answer

Correct option: C.

Both $(a)$ and $(b).$

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MCQ 531 Mark

Efficiency $(\eta)$ of the heat engine in thermodynamics can be defined as:

A
$\eta=\frac{\text{W}}{\text{Q}_2}$
B
$\eta=1-\frac{\text{Q}_1}{\text{Q}_2}$
✓
$\eta=\frac{\text{W}}{\text{Q}_1}$
D
None of these.

Answer

Correct option: C.

$\eta=\frac{\text{W}}{\text{Q}_1}$

For heat engine, $Q_1 = W + Q_2$
$\Rightarrow W = Q_1 - Q_2$
$Q_2$ is heat rejected to the environment.
So, $\eta=\frac{\text{Q}_1-\text{Q}_2}{\text{Q}_1}=\frac{\text{W}}{\text{Q}_1}$

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MCQ 541 Mark

For Carnot engine, which process should be chosen to take the working substance from $T_1$ to $T_2$ or vice$-$versa?

A
Isochoric.
B
Isothermal.
✓
Adiabatic.
D
Isobaric.

Answer

Correct option: C.

Adiabatic.

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MCQ 551 Mark

For a gas, $\gamma=1.4.$ Then Atomicity, $C_P$ and $C_V$ of the gas are:

A
Monoatomic, $\frac52\text{R},\frac32\text{R}$
B
Monoatomic, $\frac72\text{R},\frac52\text{R}$
✓
Diatomic, $\frac{7}{2}\text{R},\frac52\text{R}$
D
Triatomic, $\frac72\text{R},\frac52\text{R}$

Answer

Correct option: C.

Diatomic, $\frac{7}{2}\text{R},\frac52\text{R}$

From $\gamma=\Big(1+\frac2{\text{n}}\Big)=1.4$
We get $n = 5,$ which is the number of degrees of freedom of a diatomic gas.
$\text{C}_\text{v}=\frac{\text{n}}{2}\text{R}=\frac{5}{2}\text{R}$
$\text{C}_\text{P}=\Big(\frac{\text{n}}{2}+1\Big)\text{R}=\frac{7}{2}\text{R}$

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MCQ 561 Mark

Efficiency of engine is $\eta_1$ at $T_1 = 200^\circ C$ and $T_2 = 0^\circ C$ and $\eta_2$ at $T_1 = 0^\circ C$ and $T_2 = 200^\circ K.$ Find the ratio of $\frac{\eta_1}{\eta_2}.$

A
$1.00$
B
$0.721$
✓
$0.577$
D
$0.34$

Answer

Correct option: C.

$0.577$

$\eta_1=1-\frac{273+0}{200+273}=\frac{200}{473}$
$\eta_2=1-\frac{-200+273}{0+27 3}=\frac{200}{273}$
$\frac{\eta_1}{\eta_2\text{}}=\frac{200}{473}\times\frac{273 }{200}=\frac{273}{473}=0.577$

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MCQ 571 Mark

Choose the correct option:

A
Zeroth law gives the concept of temperature.
B
Temperature measures the 'hotness' of the body.
C
Heat flows from higher temperature to lower temperature until thermal equilibrium is attained.
✓
All of the above.

Answer

Correct option: D.

All of the above.

Heat flows from body $A$ to body $B$ because temperature of body $A$ is higher. At thermal equilibrium, $\text{T}_\text{A}'=\text{T}_\text{B}'$

$A$ in equilibrium with $C$	$A$ in equilibrium with $B$
$B$ in equilibrium with $C$

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MCQ 581 Mark

For a gas, $y = 1.4$ then atomicity, $C_p$ and $C_v$ of the gas are:

A
Monoatomic $\frac52\text{R},\frac32\text{R}$
B
Monoatomic $\frac72\text{R},\frac52\text{R}$
✓
Diatomic $\frac72\text{R},\frac52\text{R}$
D
Triatomic $\frac72\text{R},\frac52\text{R}$

Answer

Correct option: C.

Diatomic $\frac72\text{R},\frac52\text{R}$

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MCQ 591 Mark

If $150J$ of heat is added to a system and the work done by the system is $110J,$ then change in internal energy will be:

✓
$40J.$
B
$110J.$
C
$150J.$
D
$260J.$

Answer

Correct option: A.

$40J.$

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MCQ 601 Mark

An ideal gas undergoes four different processes from thesame initial state $($Fig.$)$. Four processes are adiabatic, isothermal, isobaric and isochoric. Out of $1, 2, 3$ and $4$ whichone is adiabatic.

A
$4$
B
$3$
✓
$2$
D
$1$

Answer

Correct option: C.

$2$

$4$ is isobaric process, $1$ is isochoric. out of $3$ and $2, 3$ has the smaller slope $($magnitude$)$ hence is isothermal. Remaining process $2$ is adiabatic.

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MCQ 611 Mark

A mixture of gases undergoing explosive chemical reaction:

A
Is not in equilibrium state during explosion.
B
May have variable temperature and pressure values during explosion.
C
Finally the gas will attained equilibrium state with its surroundings.
✓
All of the above.

Answer

Correct option: D.

All of the above.

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MCQ 621 Mark

The efficiency of a Carnot's engine working between steam point and ice point is:

✓
$26.81\%$
B
$29\%$
C
$30\%$
D
$10\%$

Answer

Correct option: A.

$26.81\%$

$T_1 = (100 + 273) = 373K$
$T_2 = (0 + 273) = 273K$
Efficiency $(\eta)=1-\frac{\text{T}_2}{\text{T}_1}$
$=1-\frac{273}{373}=\frac{100}{373}$
$\%\eta=\frac{100}{373}\times100$
$=26.81\%$

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MCQ 631 Mark

The given quantity of an ideal gas is at pressure $P$ and absolute Temperature $T.$ The isothermal bulk Modulus of the gas is:

A
$\frac{2}{4}\text{R}$
✓
$\text{P}$
C
$\frac32\text{P}$
D
$2\text{P}$

Answer

Correct option: B.

$\text{P}$

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MCQ 641 Mark

A given quantity of an ideal gas is at pressure $P$ and absolute temperature $T.$ The isothermal bulk modulus of the gas is:

A
$\frac23\text{P}$
✓
$\text{P}$
C
$\frac23\text{P}$
D
$\text{2P}$

Answer

Correct option: B.

$\text{P}$

$K_i = P =$ the pressure exerted by the gas.

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MCQ 651 Mark

Three copper blocks of masses $M_1, M_2$ and $M_3\ kg$ respectively are brought into thermal contact till they reach equilibrium. Before contact, they were at $T_1, T_2, T_3 (T_1 > T_2 > T_3).$ Assuming there is no heat loss to the surroundings, the equilibrium temprature $T$ is $(s$ is specific heat of copper$)$

A
$\text{T}=\frac{\text{T}_{1}+\text{T}_{2}+\text{T}_{3}}{3}$
✓
$\text{T}=\frac{\text{M}_{1}\text{T}_{1}+\text{M}_{2}\text{T}_{2}+\text{M}_{3}\text{T}_{3}}{\text{M}_{1}+\text{M}_{2}+\text{M}_{3}}$
C
$\text{T}=\frac{\text{M}_{1}\text{T}_{1}+\text{M}_{2}\text{T}_{2}+\text{M}_{3}\text{T}_{3}}{3(\text{M}_{1}+\text{M}_{2}+\text{M}_{3})}$
D
$\text{T}=\frac{\text{M}_{1}\text{T}_{1}\text{S}+\text{M}_{2}\text{T}_{2}\text{S}+\text{M}_{3}\text{T}_{3}\text{S}}{\text{M}_{1}+\text{M}_{2}+\text{M}_{3}}$

Answer

Correct option: B.

$\text{T}=\frac{\text{M}_{1}\text{T}_{1}+\text{M}_{2}\text{T}_{2}+\text{M}_{3}\text{T}_{3}}{\text{M}_{1}+\text{M}_{2}+\text{M}_{3}}$

Let the equilibrium tempreature of the system $= T$
Let $\text{T}_{1}\text{T}_{2}<\text{T}<\text{T}_{3}$
As there is no loss to the surrounding.
Heat lost by $\text{M}_{3}=$ Heat gain by $\text{M}_{1}+$ Heat gain by $\text{M}_{2}$
$\text{M}_{3}\text{s}(\text{T}_{3}-\text{T})=\text{M}_{1}\text{s}(\text{T}-\text{T}_{1})+\text{M}_{2}\text{s}(\text{T}-\text{T}_{2})$
$\text{M}_{3}\text{s}\text{T}_{3}-\text{M}_{3}\text{s}\text{T}=\text{M}_{1}\text{s}\text{T}=\text{M}_{1}\text{s}\text{T}-\text{M}_{1}\text{s}\text{T}_{1}+\text{M}_{2}\text{s}\text{T}-\text{M}_{2}\text{s}\text{T}_{2}$
$\text{T}(\text{M}_{3}+\text{M}_{1}+\text{M}_{2})=[\text{M}_{3}\text{T}_{3}+\text{M}_{1}\text{T}_{1}+\text{M}_{2}\text{T}_{2}]$
$\text{T}=\frac{\text{M}_{1}\text{T}_{1}+\text{M}_{2}\text{T}_{2}+\text{M}_{3}\text{T}_{3}}{\text{M}_{1}+\text{M}_{2}+\text{M}_{3}}$
Hence verifies option $(b).$

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MCQ 661 Mark

According to first law of thermodynamics,

A
Heat neither enters nor leaves the system.
B
Heat is constant in isothermal system.
✓
Energy is conserved.
D
None of these.

Answer

Correct option: C.

Energy is conserved.

First law of ther modynamics is the principle of conservation of energy.

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MCQ 671 Mark

An engine has an efficiency of $\frac16$ when the temperature of sink is reduced by $62^\circ C,$ its efficiency is doubled, temperature of the source is:

A
$37^\circ C.$
B
$62^\circ C.$
✓
$99^\circ C.$
D
$124^\circ C.$

Answer

Correct option: C.

$99^\circ C.$

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MCQ 681 Mark

The internal energy of an ideal gas depends on:

A
Pressure.
B
Volume.
✓
Temperature.
D
Size of molecules.

Answer

Correct option: C.

Temperature.

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MCQ 691 Mark

$(\Delta\text{Q}-\Delta\text{W})$ is:

A
Path dependent.
B
Path independent.
C
Equal to $\Delta\text{U}.$
✓
Both $(b)$ and $(c).$

Answer

Correct option: D.

Both $(b)$ and $(c).$

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Physics M.C.Q (1 Marks)