Thermodynamics Test

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Thermodynamics Test - 81

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Weekly Quiz Competition

Question 1
1 / -0

If the slope for isotherm is $$X$$ and the slope for adiabatic is $$Y$$ then

A
$$X=\gamma Y$$

B
$$Y=\gamma X$$

C
$$X=Y$$

D
$${ X }^{ \gamma }=Y$$

Solution
Question 2
1 / -0

When gas in a vessel expands, its thermal energy decreases. The process involved is

A
Isobaric

B
Isochoric

C
Isothermal

D
Adiabatic

Solution
Question 3
1 / -0

An ideal gas at $${ 27 }^{ \circ }C$$ is compressed adiabatically to $$\dfrac { 8 }{ 27 } $$ of its original volume. If $$\gamma =\dfrac { 5 }{ 3 } $$, then the rise in temperature is

A
450 K

B
375 K

C
225 K

D
405 K

Solution
Question 4
1 / -0

An ideal gas of volume $$V$$ and pressure $$P$$ expands isothermally to volume $$16V$$ and then compressed adiabatically to volume $$V$$. The final pressure of gas is $$[\gamma = 1.5]$$

A
$$P$$

B
$$3P$$

C
$$4P$$

D
$$6P$$

Solution
Question 5
1 / -0

For an adiabatic expansion of a perfect gas, the value of $$\dfrac {\triangle P}{ P }$$ is equal to

A
$$-\sqrt { \gamma } \dfrac { \Delta V }{ V } $$

B
$$- \dfrac { \Delta V }{ V } $$

C
$$-{ \gamma } \dfrac { \Delta V }{ V } $$

D
$$-{ \gamma }^{ 2 } \dfrac { \Delta V }{ V } $$

Solution
Question 6
1 / -0

Helium at $$27^0C$$ has a volume of $$8$$ litres. It is suddenly compressed to a volume of $$1$$ litre. The temperature of the gas will be [$$\gamma= 5/3$$]

A
$$108^oC$$

B
$$9327^oC$$

C
$$927^oC$$

D
$$1200^oC$$

Solution
Question 7
1 / -0

Three Carnot engines operate in series between a heat source at a temperature $$T_{1}$$ and a heat sink at temperature $$T_{4}$$ (see figure). There are two other reservoirs at temperature $$T_{2}$$, and $$T_{3}$$, as shown, with $$T_{2} > T_{2} > T_{3} > T_{4}$$. The three engines are equally efficient if__?

A
$$T_{2} = (T_{1}^{2}T_{4})^{1/3} : T_{3} = (T_{1} T_{4}^{2})^{1/3}$$

B
$$T_{2} = (T_{1}T_{4}^{2})^{1/3} : T_{3} = (T_{1}^{2} T_{4})^{1/3}$$

C
$$T_{2} = (T_{1}^{3}T_{4})^{1/4} : T_{3} = (T_{1} T_{4}^{3})^{1/4}$$

D
$$T_{2} = (T_{1}T_{4})^{1/2} : T_{3} = (T_{1}^{2} T_{4})^{1/3}$$

Solution

Given: $$t_{1} = 1 - \dfrac {T_{2}}{T_{1}} = 1 - \dfrac {T_{2}}{T_{2}} = 1 - \dfrac {T_{4}}{T_{3}}$$

$$\Rightarrow \dfrac {T_{2}}{T_{1}} = \dfrac {T_{3}}{T_{2}} = \dfrac {T_{4}}{T_{3}}$$

$$\Rightarrow T_{2} = \sqrt {T_{1} T_{3}} = \sqrt {T_{1} \sqrt {T_{2}T_{4}}}$$

$$\Rightarrow T_2^{(1 - 1/4)} = T_1^{1/2} T_4^{ 1/4}$$

$$\Rightarrow T_{2}^{3/4} = T_{1}^{1/2} T_{4}^{1/4}$$

$$\Rightarrow T_{2} = (T_{1}^{2} T_{4})^{1/3}$$

$$T_3 = \sqrt{T_2 T_4} = \sqrt{(T_{1}^{2} T_{4})^{1/3} T_4} = T_{1}^{1/3} T_{4}^{2/3}$$.
Question 8
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Choose the incorrect statement from the following.

A
The efficiency of a heat engine can be 1, but the coefficient of performance of a refrigeration can never be infinity.

B
the first law of thermodynamics is basically the principle of conservation of energy.

C
the second law of thermodynamics does not allow several phenomena consistent with the first law.

D
A process, that rejects heat to a hotter object is impossible.

Solution
Question 9
1 / -0

Which of the following is incorrect?

A
If two system $$A$$ and $$B$$ are in thermal equilibrium with system $$C$$ separately, then $$A$$ and $$B$$ will be in thermal equilibrium

B
Zeroth law of thermodynamics defines temperature

C
Temperature does not determine the direction of flow of heat when two bodies are placed in thermal contact

D
Internal energy of an ideal gas depends on the state of the system

Solution
Question 10
1 / -0

The slope of indicator curve in adiabatic change relative to volume axis is -

A
$$P/V^y$$

B
$$P^y/V^{y-1}$$

C
$$\dfrac{P}{y^(V)}$$

D
$$-\gamma(\dfrac{P}{V})$$

Solution