Thermodynamics Test

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Thermodynamics Test - 60

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Weekly Quiz Competition

Question 1
1 / -0

A block of steel heated to 100 .c left in a room to to cool . Which of the curves shown in figure represented the correct behaviour?

A
B

B
C

C
A

D
none

Solution
Question 2
1 / -0

An ideal monoatomic gas undergoes expansion according to $$P=bV$$,Where 'b' is a constant.Molar heat capacity of gas in the process is

A
$$\dfrac {3R} {2}$$

B
$$2R$$

C
$$\dfrac {5R} {2}$$

D
$$3R$$

Solution

$$P=bv$$
$$ \Rightarrow p{v^{ - 1}} = const$$
$$c = \left( {\frac{f}{2} + \frac{1}{{1 - x}}} \right)R$$
$$\left( {x - 1} \right)$$
$$ = \left( {\frac{3}{2} + \frac{1}{2}} \right)R$$
$$=c=2R$$
Hence,
option $$(B)$$ is correct answer.
Question 3
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A gas occupies a volume of 10 ltrs at $$27^oC$$.The kevin temperature it should be cooled isobarically to reduce its volume to 0.25 of the initial value is

A
75 K

B
300 K

C
150 K

D
$$150^oC$$

Solution
Question 4
1 / -0

A monoatomic gas undergoes a thermodynamic process $${p^2} = cT$$ where $$c$$ is a constant. Molar heat capacity of the gas for this process is

A
$$\dfrac{{3R}}{2}$$

B
$$2R$$

C
$$\dfrac{{5R}}{2}$$

D
$$3R$$

Solution
Question 5
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The volume of a poly-atomic gas $$\left( {y = \dfrac{4}{3}} \right)$$ compressed adiabatically to $$\dfrac{1}{{{8^{th}}}}$$ of the orignal volume. if the orignal pressure of the gas is $${p_0}$$ the new pressure will be:

A
$$8\,{p_0}$$

B
$$16\,{p_0}$$

C
$$6\,{p_0}$$

D
$$2\,{p_0}$$

Solution

Given,
$$\gamma=\dfrac{4}{3}$$
$$P_0=$$ initial pressure
$$V_2=\dfrac{V_1}{8}$$
$$P_0=$$ final pressure
For poly adiabatically,
$$PV^{\gamma}=constant$$

$$P_2V_2^{\gamma}=P_1V_1^{\gamma}$$

$$P_2=P_0(\dfrac{V_1}{V_2})^{\gamma}=P_0(\dfrac{V_1}{V_1/8})^{4/3}$$

$$P_2=P_0(8)^{4/3}=16P_0$$

The correct option is B.
Question 6
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the volume of a gas expands by 0.25 $${m^3}$$ at a constant pressure of $${10^3}N/{m^2}$$. The work done is equal to

A
2.5 erg

B
250 j

C
250 w

D
250 N

Solution

Given,
$$d V=0.25m^3$$
$$P=10^3N/m^2$$
Work done, $$W=\int PdV$$
$$W=0.25\times 1000=250J$$
The correct option is B.
Question 7
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A polytropic process for an ideal gas is represented by equation $$=PV^n$$ constant. If $$\gamma $$ is ratio of specific heats $$(\frac {C_p} {C_v})$$ . then value of n for which molar heat capacity of the process is negative, is given as

A
$$\gamma > n$$

B
$$\gamma > n > 1$$

C
$$n > \gamma $$

D
none as it is not possible

Solution

$$P{V^n} = const$$
$$C = \dfrac{{fR}}{2} + \dfrac{R}{{1 - n}} < 0$$
$$ \Rightarrow CV + \dfrac{R}{{n - 1}} < 0$$
$$ \Rightarrow CV < \dfrac{R}{{n - 1}}$$ $$$$
$$\because CV > 0$$
$$\therefore n - 1 > 0$$
$$ \Rightarrow n > 1$$
$$ \Rightarrow \left( {n - 1} \right) < \dfrac{R}{{CV}}$$
$$ \Rightarrow n < \dfrac{{R + CV}}{{CV}}$$
$$ \Rightarrow n < \dfrac{{CP}}{{CV}}$$
$$ \Rightarrow n < \gamma $$
$$\therefore \gamma > n > 1$$
Hence,
option $$(B)$$ is correct answer.
Question 8
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One mole of an ideal gas at a temperature $$T_1 K$$ expands slowly according to the law $$\dfrac{P}{V}=$$ constant. Its final temperature is $$T_2 K.$$ The work done by the gas is:

A
$$R(T_2-T_1)$$

B
$$2R(T_2-T_1)$$

C
$$\dfrac{R}{2}(T_2-T_1)$$

D
$$\dfrac{2R}{3}(T_2-T_1)$$

Solution
Question 9
1 / -0

P-V diagram of an ideal gas is as shown in figure. work done by the gas the process ABCD is:

A
$$4{ P }_{ 0 }{ V }_{ 0 }$$

B
$${ 2P }_{ 0 }{ V }_{ 0 }$$

C
$$3{ P }_{ 0 }{ V }_{ 0 }$$

D
$${ P }_{ 0 }{ V }_{ 0 }$$

Solution

Work done for $$PV$$ curve

is, area under the $$PV$$ curve

Work done for $$AB$$= $$P(dV)$$

$$- (P_o)* V_o= -(P_o V_o)$$........$$(i)$$

Work done for $$BC$$, $$(dV)= o$$

So, work done for $$BC = 0$$.........$$(ii)$$

Work done for $$CD$$= $$(2P_o)*(2V_o)= (4P_o V_o)$$......$$(ii)$$

Total Work done = adding euations $$ (i), (ii), and (ii)$$ we get,

Work done for $$ABCD = (3P_o V_o) $$
Question 10
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The temperature below which a gas cannot be liquefied is called

A
Inversion temperature

B
Neutral temperature

C
Critical temperature

D
Curie temperature

Solution

Solution: The temperature at which or above which the vapors of the substance cannot be liquified regardless of the how much pressure is applied is called a critical temperature. Each and every substance have a critical temperature.
Hence, the correct option is (C).