Thermodynamics Test

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Thermodynamics Test - 49

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Weekly Quiz Competition

Question 1
1 / -0

A heat engine is supplied with 250 kJ/s of heat at a constant fixed temperature of $$227^0C$$; the heat is rejected at $$27^0C$$, the cycle is reversible, then what amount of heat is rejected?

A
24kJ/s

B
223kJ/s

C
150kJ/s

D
none of the above

Solution

The temperature in kelvin scales are $$T_1=273+27=300K,T_2=273+237=500K$$

$$T_1$$is temperature of sink And$$T_2$$ is temperature of source hence by efficiency we get

$$\eta=1-\dfrac{T_1}{T_2}=1-\dfrac{Q_1}{Q_2}$$

$$Q_1=\dfrac{T_1}{T_2}*Q_2=\dfrac{300}{500}*250=150kW$$
Question 2
1 / -0

An ideal gas expands according to the law $$pV^2$$= const. The molar heat capacity C is

A
$$C_v $$+ R

B
$$C_v $$- R

C
$$C_v $$+ 2R

D
$$C_v $$- 3R

Solution

The correct answer is option(B).
Molar heat capacity,
$$C=C_V+\dfrac R{1-K}=C_V+\dfrac R{1-2}=C_V-R$$
Question 3
1 / -0

A number of small drops of mercury coalesce adiabatically to form a single drop. The temperature of drop

A
Increases

B
Is infinite

C
Remains unchanged

D
May decrease or increase depending upon size

Solution

Hint: For the adiabatic process change in heat is 0.
Question 4
1 / -0

A gas is compared adiabatically till its temperature is doubled. The ratio of his final volume to its initial volume will be :

A
Between $$ \frac {3}{2} $$ and 2.

B
$$ \frac {1}{2} $$

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

D
Less than $$ \frac {1}{2} $$

Solution

Using the relation,
$$ T_1 V_1^{1- \gamma} = T_2 V_2^{1- \gamma }$$

$$ \dfrac {V_2}{V} = \left( \dfrac {T_1}{T_2} \right)^{ 1 - \gamma} = \left( \dfrac {T_1}{2T_2} \right)^{ 1 - \gamma} $$

or $$ \dfrac {1}{(2)^{ 1 - \gamma}} > \dfrac {1}{2} $$
Question 5
1 / -0

When an ideal gas at pressure p, temperature T and volume V is isothermally compressed to V/n, its pressure becomes $$\displaystyle p_i$$. If the gas is compressed adiabatically to $$\displaystyle \frac{V}{n}$$, its pressure becomes $$\displaystyle p_a$$. The ratio $$\displaystyle p_i/p_a$$ is $$\displaystyle \left( \gamma = \frac{C_p}{C_V} \right)$$

A
1

B
n

C
$$\displaystyle n^{\gamma}$$

D
$$\displaystyle n^{1- \gamma}$$

Solution

For isothermal process,
$$\displaystyle pV=$$ constant.
Therefore $$\displaystyle p_iV_i = pV$$
or $$\displaystyle p_i \frac{V}{n} = pV$$
or $$\displaystyle p_i =np$$ .....(i)
For adiabatic process, $$\displaystyle pV^{\gamma} =$$ constant.
Therefore
$$\displaystyle p_a(V_a)^{\gamma} = pV^{\gamma}$$
or $$\displaystyle p_a \left( \frac{V_a}{n} \right)^{\gamma} = pV^{\gamma}$$
or $$\displaystyle p_a= n^{\gamma} p$$
From Eqs. (i) and (ii), we get
$$\displaystyle \frac{p_i}{p_a} = \frac{n}{n^\gamma} = n^{(1- \gamma)}$$
Question 6
1 / -0

In an adiabatic process.

A
Temperature remains constant

B
Pressure remains constant

C
Volume remains constant

D
There is no transfer of heat

Solution

In adiabatic process there is no heat transfer i.e $$\Delta Q=0$$
Question 7
1 / -0

During one cycle of a heat engine $$2000$$ calories of heat is supplied and $$1500$$ calories rejected. The amount of work done equals:

A
$$2093\ J$$

B
$$4186\ J$$

C
$$1042\ J$$

D
$$0$$

Solution

Work done equals the difference of heat supplied to the heat lost.
$$W = Q_{in} - Q_{out}$$
$$ = 2000-1500$$
$$=500\ cal$$
$$=4.186 \times 500 J$$
$$=2093\ J$$
Question 8
1 / -0

A gas is compressed at constant pressure $$ 50 N/m^2$$ from a volume of $$ 0m^3$$ to a volume $$ 4m^3 . $$ Energy $$100 J$$ is then added to the gas by heating. Its internal energy is :

A
Increased by $$100\ J$$

B
Increased by $$200\ J$$

C
Decreased by $$100\ J$$

D
Increased by $$400\ J$$

Solution

Change in volume $$ \triangle V_2 - V_1 = 4 - 10 = -6 m^3 $$
A volume decreases, work is done on the gas and so it is negative.
$$ W = p \triangle V = 50 \times (-6) = -300 J $$
Additional heat supplied $$ (G = + 100 J ) . $$ So, for the first law of thermodynamics change in external energy is given by
$$ \triangle U = Q - W = 100-(-300) = 400J $$
Internal energy increases by 400 J.
Question 9
1 / -0

In the P - V diagram below the dashed curved line is an adiabatic process. For a process that is described by a straight line joining two points $$X$$ and $$Y$$ on the adiabat (solid line in the diagram) heat is : (hint : Consider the variations in temperature from $$X$$ to $$Y$$ along the straight line)

A
Absorbed throughout from $$X$$ to $$Y$$

B
Released throughout from $$X$$ to $$Y$$

C
Absorbed from $$X$$ up to an intermediate point $$Z$$ (not shown in the figure) and then released from $$Z$$ to $$Y$$

D
Released from $$X$$ up to an intermediate point $$Z$$ (not shown in the figure) and then absorbed from $$Z$$ to $$Y$$

Solution

Since from point X to Y ,the gas is compressed and since in adiabatic process no heat is lost so the Temperature at Y is greater than the temperature at X
Question 10
1 / -0

A heat engine is $$20$$% efficient. If the engine does $$500\ J$$ of work every second, how much heat does the engine exhaust every second?

A
$$2000\ J$$

B
$$2500\ J$$

C
$$400\ J$$

D
$$500\ J$$

Solution

Efficiency in percentage is defined as:
$$\eta = \cfrac{\text{Work Done}}{\text{Heat energy supplied}} \times 100$$
$$20 = \cfrac{500}{E_{in}} \times 100$$
$$E_{in} = 2500\ J$$

Heat energy exhausted is the difference of the heat energy supplied and effective work done. Hence, heat exhausted is given by:
$$H = 2500-500 = 2000\ J$$

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Thermodynamics Test - 49

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Thermodynamics Test - 49

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Question 1

24kJ/s

223kJ/s

150kJ/s

none of the above

Solution

Question 2

$$C_v $$+ R

$$C_v $$- R

$$C_v $$+ 2R

$$C_v $$- 3R

Solution

Question 3

Increases

Is infinite

Remains unchanged

May decrease or increase depending upon size

Solution

Question 4

Between $$ \frac {3}{2} $$ and 2.

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

More than $$ \frac {1}{2} $$

Less than $$ \frac {1}{2} $$

Solution

Question 5

1

n

$$\displaystyle n^{\gamma}$$

$$\displaystyle n^{1- \gamma}$$

Solution

Question 6

Temperature remains constant

Pressure remains constant

Volume remains constant

There is no transfer of heat

Solution

Question 7

$$2093\ J$$

$$4186\ J$$

$$1042\ J$$

$$0$$

Solution

Question 8

Increased by $$100\ J$$

Increased by $$200\ J$$

Decreased by $$100\ J$$

Increased by $$400\ J$$

Solution

Question 9

Absorbed throughout from $$X$$ to $$Y$$

Released throughout from $$X$$ to $$Y$$

Absorbed from $$X$$ up to an intermediate point $$Z$$ (not shown in the figure) and then released from $$Z$$ to $$Y$$

Released from $$X$$ up to an intermediate point $$Z$$ (not shown in the figure) and then absorbed from $$Z$$ to $$Y$$

Solution

Question 10

$$2000\ J$$

$$2500\ J$$

$$400\ J$$

$$500\ J$$

Solution

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