Thermodynamics Test

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Thermodynamics Test - 80

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Weekly Quiz Competition

Question 1
1 / -0

The given $$p-V$$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

A
$$p_{0}V_{0}$$

B
$$\left (\dfrac {13}{2}\right )p_{0}V_{0}$$

C
$$\left (\dfrac {11}{2}\right )p_{0}V_{0}$$

D
$$4p_{0}V_{0}$$

Solution
Question 2
1 / -0

One mole of a monatomic gas and one mole of a diatomic gas are initially in the same state Both gases are expanded isothermally and then adiabatically such that they acquire the same final state.Choose the correct statement.

A
Work done by diatomic gas is more than that by monatomic gas.

B
work done by monatomic gas is more than that by diatomic gas.

C
wark done by both the gases are equal.

D
change in internal energies of both the gases are equal.

Solution
Question 3
1 / -0

An ideal gass undergoes an adiabatic process obeying the ralation P$${ V }^{ 4/3 }$$=constant. If its initial temperature is 300 KI and then its pressure is increased unto four times its initial value, then the final temoerature is ( in keliven)

A
300$$\sqrt { 2 } $$

B
300$$\sqrt [ 3 ]{ 2 } $$

C
600

D
1200

Solution
Question 4
1 / -0

The specific heat of hydrogen gas at constant pressure is $$C_{P} = 3.4\times 10^{3} cal/ kg^{\circ}C$$ and at constant volume is $$C_{V} = 2.4\times 10^{3} cal/ kg^{\circ}C$$. If one kilogram hydrogen gas is heated from $$10^{\circ}C$$ to $$20^{\circ}C$$ at constant pressure, the external work done on the gas to maintain it at constant pressure is

A
$$10^{5} cal$$

B
$$10^{4} cal$$

C
$$10^{3} cal$$

D
$$5\times 10^{3} cal$$

Solution
Question 5
1 / -0

The temperature of an open room of volume $$30$$ m$$^3$$ increases from $$17^\circ$$C to $$27^\circ$$C due to the sunshine. The atmospheric pressure in the room remains $$1 \times 10^5$$ Pa. If $$n_i$$ and $$n_f$$ are the number of molecules in the room before and after heating, then $$n_i - n_f$$ will be:

A
$$ - 2.5 \times {10^{25}}$$

B
$$ - 1.61 \times {10^{23}}$$

C
$$1.38 \times {10^{23}}$$

D
$$2.5 \times {10^{25}}$$

Solution
Question 6
1 / -0

An ideal gas has a molar heat capacity pressure Cp=2.5R
. The gas is kept in a closed volume of 0.083m3
at a temperature of 300∘K
and a pressure of 105N/m2
. 200J
of heat is supplied to the gas. Calculate the final temperature and pressure of the gas.

A
Initial pressuer of the gas is $$1.06\times10^5N/m^2$$

B
Final temperature of the gas is $$1000K$$.

C
Final pressure of the gas is $$1.06\times10^5N/m^2$$

D
Work done by gas is $$9.94\times10^3J$$
Question 7
1 / -0

Radius of two spheres of same material are 1 and 4 m respectively and their temperature are $$4\times 10^{3}$$ and $$2\times 10^{3}$$ K respectively. Then ratio of emitted energy of spheres per sec. will be

A
1 : 2

B
2 : 1

C
1 : 1

D
4 : 1

Solution

$$\begin{array}{l} \dfrac { { { U_{ 1 } } } }{ { { U_{ 2 } } } } =\dfrac { { { A_{ 1 } }T_{ 1 }^{ 4 } } }{ { { A_{ 2 } }T_{ 2 }^{ 4 } } } =\dfrac { { E_{ 1 }^{ 2 } } }{ { E_{ 2 }^{ 2 } } } \cdot \left( { \dfrac { { { T_{ 1 } } } }{ { { T_{ 2 } } } } } \right) =\dfrac { 1 }{ { 16 } } \times \dfrac { { { { \left( { 4\times { { 10 }^{ 3 } } } \right) }^{ 4 } } } }{ { { { \left( { 2\times { { 10 }^{ 3 } } } \right) }^{ 4 } } } } \\ =\dfrac { { 256 } }{ { 16 } } \times \dfrac { 1 }{ { 16 } } =\dfrac { 1 }{ 1 } =1:1 \end{array}$$
Question 8
1 / -0

The pressure and density of a diatomic gas (y=7/5) changes adiabatically from (P,p) to $$\left( { P }^{ ' },{ p }^{ ' } \right) $$. If $${ P }^{ ' }/P$$=32, then $$\left( { P }^{ ' }{ /P } \right) $$ should be

A
$$\dfrac{1}{128}$$

B
32

C
128

D
none

Solution
Question 9
1 / -0

A thermodynamical process is shown in the figure. The pressure and volumes corresponding to some points in the figure are$${ P }_{ A } = 3 \times {10}^{4} Pa$$ $${ V }_{A} = 2 \times {10}^{-3} { m }^{3} $$$${ P }_{ B } = 8 \times {10}^{4} Pa$$ $${ V }_{D} = 5 \times {10}^{-3} { m }^{3} $$In the process $$AB$$, $$600 J$$ of heat is added to the system and in process $$BC 200 J$$ of heat is added to the system. The change in internal energy of the system in process $$AC$$ would be

A
$$560 J$$

B
$$800 J$$

C
$$600 J$$

D
$$640 J$$

Solution
Question 10
1 / -0

In adiabatic process, volume of monoatomic gas increases by 6% then find percentage change in temperature.

A
-2%

B
-4%

C
2%

D
4%

Solution