Thermodynamics Test

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Thermodynamics Test - 36

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Question 1
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A closed container is fully insulated from outside. One half of it is filled with an ideal gas X separated by a plate P from the other half Y which contains a vacuum as shown in figure. When O is removed , X moves into Y . Which of the following statements is correct

A
No work is done by X

B
X decreases in temperature

C
X increases in internal energy

D
X doubles in pressure

Solution

Work done by a gas is given by:
$$w = \int PdV$$
Work done by X is against vacuum, hence P = 0;
$$w = \int PdV = \int 0dV = 0$$
Hence no work is done by or done on X.
Question 2
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An ideal gas is taken from point A to point C on P-V diagram through two process AOC and ABC as shown in the figure . Process AOC is isothermic

A
Process AOC requires more heat than process ABC

B
Process ABC requires more heat than process AOC

C
Both process AOC & ABC require same amount of heat

D
Data is insufficient for comparison of heat requirement for the two processes

Solution

Being a state-function, change in in internal energy($$\Delta U$$) is the same for the two processes AOC and ABC, i.e. $$\Delta U_{AOC}=\Delta U_{ABC}$$
Work done=W= area under P-V diagram
Hence $$W_{AOC}>W_{ABC}$$
$$\Rightarrow \Delta U_{AOC}+W_{AOC}>\Delta U_{ABC}+W_{ABC}$$
$$\Rightarrow \Delta Q_{AOC}>\Delta Q_{ABC}$$
Question 3
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Gas in cylinder with light piston is slowly heated till all the mercury spills over.
$$ {P} _{atm} = 76\ cm $$ of Hg column
Statement 1 : The temperature of gas continuously increases.
Statement 2: According to first law of thermodynamics $$dQ = dU + dW$$ where symbols have their usual meaning.

A
Statement1 is true, statement 2 is true and statement 2 is correct explanation for statement 1

B
Statement1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement 1

C
Statement 1 is true statement 2 is false

D
Statement 1 is false , statement 2 is true

Solution

Change in temperature depends on what sort of process we allow the system to evolve through.
We only know that it is some sort of reversible expansion with decreasing pressure, i.e P decreases while V increases$$\Rightarrow$$ their product may increase or decrease or remain constant.

Applying ideal gas eqn. $$PV=nRT$$ , temperature may increase or decrease or remain constant.So statement a is false
Statement b is true as it is the statement of first law regarding conservation of energy.

Hence d is correct option
Question 4
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A process shown is shown in diagram. which of the following curves may represent the same process

A

B

C

D

Solution

In the process from A to B, the pressure tends to remain constant.
Following Charles' Law, for a constant pressure, the V-T curve is a straight line.

Similarly, from going B to C, the P-V curve is parabolic which means, that the the process is isothermal and the temperature will remain same over the period from B to C.
Thus, the option (C)
Question 5
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Directions For Questions

It is possible to make crystalline solids that are only one layer of atoms thick. Such two dimensional crystals can be created by depositing atoms on a very flat surface. The atoms in such a two dimensional crystal can move only within the plane of the crystal, At very low temperature the molar heat capacity of such a crystal is C$$_1$$ and at room temperature it is C$$_2$$

...view full instructions

How are C$$_1$$ and C$$_2$$ related?

A
$$C_1 = C_2$$

B
$$C_1 > C_2$$

C
$$C_1 < C_2$$

D
Insufficient data to reply

Solution

At low temperatures, $$C\propto T^5$$.
While at ordinary temperatures, $$C\propto T$$.
Thus $$C_1<C_2$$
Question 6
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The first law of thermodynamics can be written as $$\Delta U$$ = q +w for an ideal gas. Which of the following statements is correct?

A
$$ \Delta U $$ is always zero when no heat enters or leaves the gas.

B
$$ W $$ is the work done by the gas in this written law.

C
$$ \Delta U $$ is zero when heat is supplied and the temperature stays constant

D
$$ \Delta U = -W $$ when the temperature increases very slowly

Solution

Option:A
When no heat enters or leaves, $$\Delta Q = 0$$
Therefore, $$\Delta U = W$$
Hence, it is an incorrect option.
Option:B
It is given $$\Delta U = Q+W, So, work is done on the gas.$$
Hence, it is also an incorrect option.
Option:C
$$\Delta U = nC_v \Delta T$$
Since Temperature is constant,
$$\Delta U =0$$
Hence, C is the correct option.
Question 7
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For a monoatomic ideal gas undergoing an adiabatic change, the relation between temperature and volume $$ TV^x =constant $$ where $$x$$ is :

A
$$ \dfrac{7}{5} $$

B
$$ \dfrac{2}{5} $$

C
$$ \dfrac{2}{3} $$

D
$$ \dfrac{1}{3} $$

Solution

For an adiabatic process, $$ {T} {V}^{\gamma - 1} $$ = constant
Thus, $$x = \gamma - 1 $$
Now, for a monoatomic gas,
$$ \gamma = 1.67 $$
Thus, $$x = 0.67$$
Question 8
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The initial pressure of a gas is $$P$$. It is kept in an insulated container and suddenly its volume is reduced to one-third. Its final pressure will be

A
$$3^\gamma P$$

B
$$\displaystyle \frac{P}{3^\gamma}$$

C
$$\dfrac{P}{3}$$

D
$$3P$$

Solution

As the container is insulated which implies that no heat exchange will take place through the wall of the container. Thus the given process is an adiabatic process.

Thus, we get
$$P_1V_1^{\gamma}=P_2V_2^{\gamma}$$
or
$$P_1V_1^{\gamma}=P_2(\displaystyle\frac{V_1}{3})^{\gamma}$$

Thus, we get the final pressure as
$$P_2=P_1\times 3^\gamma$$

Option A is correct.
Question 9
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A liquid boils at such a temperature at which the saturated vapour pressure, as compared to atmospheric pressure, is

A
one-third

B
equal

C
half

D
double

Solution

The vapor pressure at which a liquid boils is equal to the atmospheric pressure.
Question 10
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Two samples of a gas A and B, initially at same temperature and pressure, are compressed to half their initial volume, A isothermally and B adiabatically. The final pressure in the two cases is related as

A
A = B

B
A > B

C
A < B

D
A$$^2$$ = B

Solution

From the PV graphs we know that the slope of an adiabatic process is more than an isothermal process. Thus for same initial conditions the pressure after compression will be more in a isothermal process than an adiabatic process. Thus A>B.