Thermodynamics Test

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Thermodynamics Test - 45

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Question 1
1 / -0

A gas does $$4.5\ J$$ of external work during adiabatic expansion. If its temperature falls by $$2\ K$$, then its internal energy will be:

A
increased by $$4.5\ J$$

B
decreased by $$4.5\ J$$

C
decreased by $$2.25\ J$$

D
increased by $$9.0\ J$$

Solution

Since it is an adiabatic expansion: $$dQ=0$$

$$\Rightarrow dU=-dW$$

$$\Rightarrow dU=-4.5\ J$$
Question 2
1 / -0

A sound wave passing through an ideal gas at NTP produces a pressure change of $$0.001$$ $$dyne/cm^2$$ during adiabatic compression. The corresponding change in temperature $$(\gamma=1.5$$ for the gas and atmospheric pressure is $$1.013\times 10^6$$ dyne$$/cm^2$$) is:

A
$$8.97\times 10^{-4}\ K$$

B
$$8.97\times 10^{-6}\ K$$

C
$$8.97\times 10^{-8}\ K$$

D
$$8.97\times 10^{-9}\ K$$

Solution

For adiabatic process, $$T^{\gamma}P^{(1-\gamma)}=$$ constant
Differentiate the equation we will get, $$T^{\gamma}(1-\gamma)P^{-\gamma} dP+\gamma P^{1-\gamma}T^{(\gamma-1)} dT=0$$
or $$dT=\dfrac{(\gamma-1)T}{\gamma P} dP=\dfrac{(1.5-1)273}{1.5\times (1.013 \times 10^6)}\times 0.001=8.97 \times 10^{-8} K$$
Question 3
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An ideal monoatomic gas at $$\displaystyle { 27 }^{ \circ }C$$ is compressed adiabatically to $$8/27$$ times of its present volume. The increase in temperature of the gas is:

A
$$\displaystyle { 375 }^{ \circ }C$$

B
$$\displaystyle { 402 }^{ \circ }C$$

C
$$\displaystyle { 175 }^{ \circ }C$$

D
$$\displaystyle { 475 }^{ \circ }C$$

Solution

Let the initial volume of the gas be $$V$$ i.e $$V_1 = V$$
Thus final volume of the gas $$V_2 = \dfrac{8}{27} V$$
Given : $$T_1 =27^o C = 300 K$$
For monoatomic gas, $$\gamma = \dfrac{5}{3}$$
Using $$TV^{\gamma } = constant$$
$$\implies$$ $$\dfrac{T_2}{T_1} = \bigg( \dfrac{V_1}{V-2}\bigg)^{\gamma- 1}$$

$$\therefore$$ $$\dfrac{T_2}{300} = \bigg( \dfrac{27}{8}\bigg)^{\frac{5}{3}- 1}$$

OR $$\dfrac{T_2}{300} = \bigg( \dfrac{27}{8}\bigg)^{\frac{2}{3}} = \bigg (\dfrac{3}{2} \bigg)^2$$ $$\implies T_2 =300 \times 2.25 = 675 K$$
$$\implies T_2 =675 - 273 = 402 ^o C$$
Thus increase in temperature $$\Delta T= T_2 - T_1 =402 - 27 =375 ^oC$$
Question 4
1 / -0

Which of the following is true in the case of an adiabatic process, where $$\gamma ={ { C }_{ p } }/{ { C }_{ v } }$$ ?

A
$${ p }^{ 1-\gamma }{ T }^{ \gamma }=$$ constant

B
$${ p }^{ \gamma }{ T }^{ 1-\gamma }=$$ constant

C
$$p{ T }^{ y }=$$ constant

D
$${ p }^{ \gamma }T=$$ constant

Solution

For adiabatic change equation of state is
$$p{ V }^{ \gamma }=$$ constant
It can also be re-written as
$$T{ V }^{ \gamma -1 }=$$ constant as $$p=\dfrac { nRT }{ V } $$
and $${ p }^{ 1-\gamma }{ T }^{ \gamma }=$$ constant as $$V=\dfrac { nRT }{ p } $$
Question 5
1 / -0

An insulated cylindrical vessel is filled with an insulated piston of negligible weight and negligible thickness at the mid point of the vessel. The cylinder contains a gas at $$\displaystyle { 0 }^{ \circ }C$$. When the gas is heated to $$\displaystyle { 100 }^{ \circ }C$$, the piston moves through a length of $$5\ cm$$. Length of the cylindrical vessel in $$cm$$ is:

A
$$13.65$$

B
$$27.3$$

C
$$38.6$$

D
$$64.6$$

Solution

The given process is isobaric.
So, $$\cfrac{V_1}{T_1}=\dfrac{V_2}{T_2}$$
$$\implies$$ $$\dfrac{A L}{273}=\dfrac{A(L+5)}{373}$$, where $$A$$ and $$L$$ are corss-section area of the piston and the initial length of the gas column respectively.
Solving, we get: $$L=13.65\ cm$$
Question 6
1 / -0

In a process, 20 joules of heat is added to an ideal gas and the gas does 12 joules of work. Which of the following is true about the internal energy of the gas during this process?

A
It has increased by 32 joules.

B
It has increased by 8 joules.

C
It has not changed.

D
It has decreased by 8 joules.

E
It has decreased by 32 joules.

Solution

From the first law of thermodynamics, change in internal energy $$(\Delta U)=$$ heat added to system $$(Q)-$$ work done by the system $$(W)$$
or $$\Delta U=20-12=8$$ J
Question 7
1 / -0

The idealized P-V diagram above shows a complete cycle through compression and expansion of a gas. The questions below relate to the processes within the cycle.
Which letter shows isothermal compression?

A
A

B
B

C
C

D
D

E
E

Solution

Isothermal compression means the system temperature remains constant. Here the part C represents the compression. The heat of the system will be kept constant during compression when allowing heat to escape from the system. Thus, option C will be correct.
Question 8
1 / -0

In a winter season, a heat pump is used to warm the room. A heat pump works 60 J on the pump while it absorbs 90 J of heat. How much heat is delivered to the house?

A
5,400 J.

B
150 J.

C
30 J.

D
1.5 J.

E
0.67 J.

Solution

Since $$60\ J$$ of the $$90\ J$$ of heat are used to do work, there are only $$30$$ joules of heat left to deliver to the house, i.e, $$90\ J - 60\ J = 30\ J$$
Question 9
1 / -0

The idealized P-V diagram above shows a complete cycle through compression and expansion of a gas. The questions below relate to the processes within the cycle.
Which letter shows an adiabatic expansion?

A
A

B
B

C
C

D
D

E
E

Solution

The volume of the gas is increasing during part A in the diagram. Thus, A part will represent the adiabatic expansion.
Question 10
1 / -0

Gas in a container absorbs 300 J of heat. After this, 100 J of work is done on it which is followed by 50 J of work done by the gas. The increase in the internal energy of the gas is:

A
450 J

B
400 J

C
350 J

D
200 J

E
100 J

Solution

Amount of heat absorbed $$Q = + 300$$ J
Net amount of work done on the gas $$W = -100 + 50 =-50$$ J
From 1st law of thermodynamics : $$Q = \Delta U + W$$
$$\therefore$$ $$300 = \Delta U + (-50)$$ $$\implies \Delta U = + 350$$ J

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Thermodynamics Test - 45

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Question 1

increased by $$4.5\ J$$

decreased by $$4.5\ J$$

decreased by $$2.25\ J$$

increased by $$9.0\ J$$

Solution

Question 2

$$8.97\times 10^{-4}\ K$$

$$8.97\times 10^{-6}\ K$$

$$8.97\times 10^{-8}\ K$$

$$8.97\times 10^{-9}\ K$$

Solution

Question 3

$$\displaystyle { 375 }^{ \circ }C$$

$$\displaystyle { 402 }^{ \circ }C$$

$$\displaystyle { 175 }^{ \circ }C$$

$$\displaystyle { 475 }^{ \circ }C$$

Solution

Question 4

$${ p }^{ 1-\gamma }{ T }^{ \gamma }=$$ constant

$${ p }^{ \gamma }{ T }^{ 1-\gamma }=$$ constant

$$p{ T }^{ y }=$$ constant

$${ p }^{ \gamma }T=$$ constant

Solution

Question 5

$$13.65$$

$$27.3$$

$$38.6$$

$$64.6$$

Solution

Question 6

It has increased by 32 joules.

It has increased by 8 joules.

It has not changed.

It has decreased by 8 joules.

It has decreased by 32 joules.

Solution

Question 7

A

B

C

D

E

Solution

Question 8

5,400 J.

150 J.

30 J.

1.5 J.

0.67 J.

Solution

Question 9

A

B

C

D

E

Solution

Question 10

450 J

400 J

350 J

200 J

100 J

Solution

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