Thermodynamics Test

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Thermodynamics Test - 85

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Question 1
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Directions For Questions

Two identical gas samples are initially at same temperature and pressure they are separately taken into two cylinders of volume V (each) and are compressed to volume $$ \frac {V}{2} $$ one isothermally and other adiabtically

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If final pressures in the process are $$ p_1 and p_2 $$ then the ratio of $$ p_1/p_2 $$ is

A
$$ 2^7 $$

B
$$ 2 $$

C
$$ \frac {1}{2} $$

D
$$ 2^{-\gamma} $$

Solution
Question 2
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In view of method of mixtures which statement is correct.
i) Net heat lost by hot body is equal to net heat gained by the cold body.
ii) Net heat lost by hot body is greater than the net heat gained by cold body.
iii) Net heat lost by hot body is less than the net heat gained by cold body.

A
(ii) and (ii) only correct

B
(ii) only correct

C
(i) only correct

D
None of these

Solution

From conservation of energy.
Heat last by heat body = Heat joined by cold body.
Ans. (C)
Question 3
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A diatomic gas initially at $$18^\circ C$$ is compressed adiabatic ally to one-eight of its original volume temperature after compression will be

A
$$10^\circ C$$

B
$$887 K$$

C
$$668K$$

D
$$144^\circ C$$

Solution
Question 4
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A gas takes part in two processes in which it is heated from the same initial state $$1$$ to the same final temperature. The processes are shown on the $$ P-V$$ diagram by the straight line $$ 1 \rightarrow 2 $$ and $$1 \rightarrow 3. \ 2$$ and $$3$$ are the points on the same isothermal curve. $$ Q_1$$ and $$Q_2 $$are the heat transfer along the two processes . then :

A
$$ Q_1 = Q_2 $$

B
$$ Q_1 < Q_2 $$

C
$$ Q_1 > Q_2 $$

D
Insufficient data

Solution
Question 5
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In $$P-V$$ graph of an ideal gas, which describe the adiabatic process :

A
$$AB$$ and $$BC$$

B
$$AB$$ and $$CD$$

C
$$AD$$ and $$BC$$

D
$$BC$$ and $$CD$$

Solution
Question 6
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Two moles of an ideal gas at a temperature of $$T=273\ K$$ was isothermally expanded $$4$$ times the initial volume and then heated isochorically, so that the final pressure becomes equal to the initial pressure. The ratio of molar specific heat capacities if total amount of heat imparted to the gas equals $$Q=27.7\ kJ$$, is

A
$$1.63$$

B
$$1.66$$

C
$$2.63$$

D
$$1.49$$

Solution
Question 7
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$$0.2$$ moles of an ideal gas, is taken round the cycle $$abc$$ as shown in the figure. The path $$b-c$$ is adiabatic process $$a-b$$ is isovolumic and $$c-a$$ is isobaric process. The temperature at $$'a'$$ and $$'b'$$ are $$T_a=300\ K$$ and $$T_b=500\ K$$ and pressure at $$'a'$$ is $$1$$ atmospheric. The volume at $$'c'$$ is :
$$\left(Given\ :\ \gamma =\dfrac {C_p}{C_v}=\dfrac {5}{3}, R=8.205\times 10^{-2}\ litre\ /atm/mol-K\right) $$

A
$$6.9\ L$$

B
$$6.68\ L$$

C
$$5.52\ L$$

D
$$5.82\ L$$

Solution

Here,

We are given with,

$$T_a=300K,T_b=500k$$
$$P_a=1atm=P_c$$
$$\gamma=\dfrac{5}{3}$$
$$R=8.205 atm.L/mol.K$$

Now,
As we know,
$$ab$$ has same volume along the process,

$$\dfrac{P_a}{P_b}=\dfrac{T_a}{T_b}$$

$$P_b=\dfrac{5}{3}atm$$

Applying ideal gas equation on point $$b$$,

$$P_bV_b=nRT_b$$

$$\dfrac{5}{3}V_b=0.2\times 8.205\times 10^{-2}\times 500$$

$$V_b=4.923 L$$

Now,
$$bc$$ is adiabatic and $$PV^{\gamma}=const$$

$$V_c^{\gamma}=\dfrac{P_b}{P_c}V_b^{\gamma}$$

Putting all the values obtained in the above equation,
We get $$V_c=6.68 L$$

Option $$\textbf B$$ is the correct answer
Question 8
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$$P.V.$$ diagram for adiabatic process is shown in the figure. Then :

A
$$v_1 > v_2 > v_3$$

B
$$v_1 < v_2 < v_3$$

C
$$v_1 > v_3 > v_2$$

D
$$none\ of\ the\ above$$
Question 9
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An ideal diatomic gas undergoes a process in which internal energy relates to its volume as $$ U= k\sqrt V$$, where k is a positive constant. Based on the given information, answer the following question.
The molar heat capacity of gas for this process is :

A
$$2.5 R$$

B
$$2 R$$

C
$$4.5 R$$

D
$$3.5 R$$

Solution
Question 10
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Consider a spherical shell of radius R at temperature T. The block radiation inside it can be considered as an ideal gas of photons with internal energy unit volume $$ u = \dfrac {U}{V} \propto T^4 $$ and pressure $$ P = \dfrac {1}{3} \left( \dfrac { U }{ V } \right) $$. If the shell now undergoes an adiabatic expansion the relation between T and R is:-

A
$$ T \propto \dfrac {1}{R^3} $$

B
$$ T \propto e^{-g} $$

C
$$ T \propto e^{-3g} $$

D
$$ T \propto \dfrac {1}{R} $$

Solution