Thermodynamics Test

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Thermodynamics Test - 78

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Question 1
1 / -0

A fixed mass of a gas is taken through a process $$A\rightarrow B\rightarrow C\rightarrow A$$. Here $$A\rightarrow B$$ is isobaric. $$B\rightarrow C$$ is adiabatic and $$C\rightarrow A$$ is isothermal. Find efficiency of the process. (take $$\gamma = 1.5)$$.

A
$$\dfrac {3 - 2ln 2}{3}$$.

B
$$\dfrac {3 - 2ln 2}{2}$$.

C
$$\dfrac {3 - ln 2}{3}$$.

D
$$\dfrac {3 - 2ln 2}{4}$$.

Solution
Question 2
1 / -0

A cyclic process $$ABCD$$ is shown in the figure P-V diagram. Which of the following curves represent the same process?

A

B

C

D

Solution

From give $$PV$$ diagram we notice that
$$A$$ to $$B$$ is pressure constant & volume in
$$D$$ to $$A$$ & $$B$$ to $$C$$ is isothermal as $$p\alpha\dfrac{1}{V}$$
$$C$$ to $$D$$ is isochoric (pressure dec) & volume constant
From $$PV=RT$$ we notice $$P=\dfrac{P}{V}T$$
i.e. if $$P$$ constant then on incorrect temperature the volume should also increase
So teh $$P.T$$ diagram given is correct for $$AB$$
$$DA$$ & $$BC$$ should be isothermal & they are also shown iso thermal in given $$P-T$$ diagram of Option $$- 1$$
$$CD$$ shown in option $$-1$$ iso choric & it should be so option $$-1$$ is correct
Question 3
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A and B are two adiabatic curves for two different gases. Then A and B corresponds to:

A
$$O_2$$ and $$N_2$$ respectively

B
$$O_2$$ and $$O_3$$ respectively

C
$$O_2$$ and $$He$$ respectively

D
$$O_2$$ and $$O$$ respectively

Solution
Question 4
1 / -0

$$300$$ gm of water at $$25^o$$C is added to $$100$$gm of ice at $$0^oC$$ . Final temperature of the mixture is:

A
$$-\dfrac{5}{3}^oC$$

B
$$-\dfrac{5}{2}^oC$$

C
$$-5^oC$$

D
$$0^oC$$

Solution

We know that latent heat of fusion of ice is $$79.7\;{\rm{Cal}}$$ per gram.
Let final temperature be T.
Then
$${m_1}S\Delta T = {m_2}L$$
$$300 \times 1 \times \left( {25 - T} \right) = 100 \times 75$$
$$\left( {25 - T} \right) = \dfrac{{100 \times 75}}{{300}}$$
$$25 - T = 25$$
$$T = 0^\circ {\rm{C}}$$
After that total energy left$$ = 4.7 \times 100$$
Total mass of water$$ = 400\;{\rm{g}}$$
Amount of water again converted into ice
$$m = \dfrac{{470}}{{79.7}}$$
$$m = 5.9\;{\rm{g}}$$
Thus whole mass is converted into water at $$0^\circ {\rm{C}}$$,and about $$5.9\;{\rm{g}}$$water is again converted into ice whose temperature is also $$0^\circ {\rm{C}}$$.

After achieving the temperature of $$0^\circ {\rm{C}}$$, latent heat of fusion is required firstly for conversion of water into ice then further lowering of temperature is possible. So the final temperature will be $$0^\circ {\rm{C}}$$.
Question 5
1 / -0

During adiabatic expansion of gas, volume increases by $$5\%$$. If $$\gamma = 3/2$$ find the percentage change in pressure?

A
$$7.5\%$$

B
$$-2.5\%$$

C
$$-15.5\%$$

D
$$-7.5\%$$

Solution
Question 6
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Two vessels $$A$$ and $$B$$ of equal volume $$V_{0}$$ are connected by a narrow tube which can be closed by a valve. The vessels are fitted with pistons which can be moved to change the volumes. Initially, the valve is open and the vessels contain an ideal gas $$(C_{P}/ C_{v} = \gamma)$$ at atmospheric pressure $$P_{0}$$ and atmospheric temperature $$T_{0}$$. The walls of the vessels $$A$$ are diathermic and those of $$B$$ are adiabatic. The valve is now closed and the pistons are slowly pulled out to increase the volumes of the vessels to double the original value.
Find the temperatures and pressures in the two vessels.

A
$$T_{0}, \dfrac {P_{0}}{3}$$ in vessel $$A$$ and $$\dfrac {T_{0}}{2^{\gamma - 1}}, \dfrac {P_{0}}{2^{\gamma}}$$.

B
$$T_{0}, \dfrac {P_{0}}{2}$$ in vessel $$A$$ and $$\dfrac {T_{0}}{2^{\gamma - 1}}, \dfrac {P_{0}}{2^{\gamma}}$$.

C
$$T_{0}, \dfrac {P_{0}}{12}$$ in vessel $$A$$ and $$\dfrac {T_{0}}{2^{\gamma - 1}}, \dfrac {P_{0}}{2^{\gamma}}$$.

D
$$T_{0}, \dfrac {P_{0}}{22}$$ in vessel $$A$$ and $$\dfrac {T_{0}}{2^{\gamma - 1}}, \dfrac {P_{0}}{2^{\gamma}}$$.

Solution
Question 7
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Five moles of hydrogen is heated through 20K under constant pressure. If R$$=$$8.312J/mole K Find the external work done.

A
831.2 J

B
83.12 J

C
166.24 J

D
16.62 J

Solution

$$\textbf{Given:- }$$Number of moles , $$n = 5 \ moles .$$
Change in temperature ,$$\Delta T = 20K$$
The pressure is constant
$$\textbf{Solution:-}$$

Work done , $$W = P\Delta V$$ ( For constant pressure )

We know , by real gas equation .

$$P\Delta V = nR\Delta T$$

Therefore , $$W = nR\Delta T$$

Putting all value in above equation :

We get ,

$$W = 5\times 8.312\times 20$$

$$W = 831.2 J$$

The external work is $$831.4 \ J.$$

$$\textbf{Hence the correct option is A}$$
Question 8
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An ideal gas has a molar heat capacity $$C_{v}$$ at constant volume. Find the molar heat capacity of this gas as a function of its volume $$V$$, if the gas undergoes the following process (a) $$T = T_{0} e^{\alpha V}$$ (b) $$P = P_{0}e^{\alpha V}$$.

A
(a) $$C_{v} + (R/ \alpha V)$$
(b) $$C_{v} + R/ (1 + \alpha V)$$.

B
(a) $$C_{v} + (R/ \alpha V)$$
(b) $$C_{v} = R/ (2 + \alpha V)$$.

C
(a) $$C_{v} + (2R/ \alpha V)$$
(b) $$C_{v} = R/ (1 + \alpha V)$$.

D
(a) $$C_{v} + (3R/ \alpha V)$$
(b) $$C_{v} = R/ (1 + \alpha V)$$.

Solution
Question 9
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The temperature $$T_1$$ and $$T_2$$ of two heat reservoirs in the ideal carnot engine are $$1500^oC$$ and $$500^oC$$ respectively.Which of these,increasing $$T_1$$ by $$100^oC$$ or decreasing $$T_2$$ by $$100^oC$$ ,would result in a greater improvement in the efficiency of the engine?

A
increasing $$T_1$$

B
decreasing $$T_2$$

C
either (a) or (b)

D
None

Solution
Question 10
1 / -0

A motor cycle engine delivers a power of 10 kW, by consuming petrol at the rate of 2.4 kg/hour. If the calorific value of petrol is 35.5 MJ /kg, the rate of heat rejection by the exhaust is

A
5.5 kW

B
13.7 kW

C
11.2 kW

D
9.7 kW

Solution