Thermodynamics Test

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Thermodynamics Test - 58

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Question 1
1 / -0

What is the ratio of work done by a ideal monoatomic gas to heat supplied to it in isobaric process.

A
$$\dfrac{3R}{2}$$

B
$$\dfrac{11}{2}$$

C
$$\dfrac{5R}{2}$$

D
$$\dfrac{13}{2}$$

Solution
Question 2
1 / -0

$$p-V$$ diagram of a diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process will be:

A
$$4R$$

B
$$2.5R$$

C
$$3R$$

D
$$\dfrac{4R}{3}$$

Solution
Question 3
1 / -0

The efficiency of a heat engine if the temperature of source $$227^0C$$ and that of sink is $$27^0C$$ nearly

A
0.4

B
0.5

C
0.6

D
0.7

Solution

The efficiency of heat engine will be$$:$$
$${T_{\sin k}}/{T_{source}}$$
$$ = \left( {273 + 27} \right)/\left( {273 + 227} \right)$$
$$ = 300/500$$
$$ = 0.6$$
So$$,$$ efficiency will be $$0.6$$
Hence,
option $$(C)$$ is correct answer.
Question 4
1 / -0

The relation between U,P and V for an ideal gas is $$U=2+3PV$$. the gas is

A
Monoatomic

B
Diatomic

C
Polyatomic

D
Either a Monoatomic or Diatomic

Solution

Given:
U = 2+ 3PV
$$\Rightarrow U = 2+ 3 nRT$$
Differentiating with respect to T,
$$\Rightarrow \dfrac{dU}{dT} = 0+ 3nR\dfrac{dT}{dT}$$
$$\Rightarrow C_v = 3nR$$
For 1 mole of a gas, n=1
$$\Rightarrow C_v =3R$$
Since the specific heat at constant volume is 3R for triatomic gas in which atoms are non linear,
Therefore, correct option is C( polyatomic).
Question 5
1 / -0

Consider a new system of units in which c (speed of light in vacuum), h(Planck's constant) and G (gravitational constant) are taken as fundamental units. Which of the following would correctly represent mass in this new system?

A
$$\sqrt{\dfrac{hc}{G}}$$

B
$$\sqrt{\dfrac{Gc}{h}}$$

C
$$\sqrt{\dfrac{hG}{c}}$$

D
$$\sqrt{hGc}$$

Solution

Consideration anew system of units in which speed of light in vaccum$$=e$$Plank's constant$$=h$$
Gravitational constant$$=G$$
Mass in the new system
$$F=\cfrac{1}{2}mv^2=h\gamma$$
Now,
Using the method of dimension we say that,
Here
$${e}=LT^{-1}$$
$$[G]=M^{-1}L^3T^{-2}$$
$$[h]=M^1L^2T^{-2}$$
Let, $$mac^xG^0h^z$$
By substituting the dimension of each quantity in both the sides
$$M=(LT^{-1})^x(M^{-1}L^3T^{-2})^y(ML^2T^{-1})^z\\M=(M^{y+z}L^{x+3y+2z}T^{x-2y-x})$$
By equating the power of $$M,L\quad and T$$ in both the sides
$$-y+z=1\\x+3y+2z=0\\-x-2y-z=0$$
By solving the above equations
We get,
$$x=\cfrac{1}{z},y=-\cfrac{1}{z},z=\cfrac{1}{z}$$
So, $$[m]=e^{1/2}G^{-1/2}h^{1/2}\\ \quad=\sqrt{\cfrac{hc}{G}}$$
Question 6
1 / -0

In an adiabatic expansion of as gas, its temperature:

A
always increase

B
always diminishes

C
remains constant

D
none of these

Solution

In an adiabatic expansion of a gas, its temperature decreases.
From 1st law of thermodynamics,
$$dU=dQ-dW$$
For adiabatic process, $$dQ=0$$
Hence, $$dU=-dW$$
Gas gas expansion, $$dW>0$$ (positive)
Therefore, $$dU$$ is less than 0, and thus internal energy decreases.
This decrease in internal energy manifest itself as a decrease in temperature T. So, the temperature decreases in an adiabatic expansion of a gas.
Question 7
1 / -0

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $$\frac { C _ { p } } { C _ { v } }$$ for the gas is

A
$$2$$

B
$$\dfrac{3}{5}$$

C
$$\dfrac{3}{2}$$

D
$$\dfrac{4}{3}$$

Solution

Given :
Pressure, P$$\alpha T^{3}$$
Solution:
In an adiabatic process,
$$T^{\gamma} P^{1-\gamma}= constant$$ ($$\gamma = \dfrac{C_p}{C_v})$$
$$\Rightarrow T \alpha \dfrac{1}{P^{\dfrac{(1-\gamma)}{(\gamma)}}}$$
$$\Rightarrow T \alpha P^\dfrac{(\gamma-1)}{\gamma}$$
$$\Rightarrow P \alpha T^\dfrac{ \gamma}{(\gamma-1)}$$
Comparing the two relations, we get
$$ 3 = \dfrac{\gamma}{(\gamma-1)}$$
$$\Rightarrow 3(\gamma -1) = \gamma$$
$$\Rightarrow 3\gamma -3 = \gamma$$
$$\Rightarrow 2\gamma = 3$$
Therefore, $$\gamma = \dfrac{3}{2} $$
Hence, correct option is C.
Question 8
1 / -0

Which is correct option for the expansion of an ideal gas under adiabatic cend?

A
$$q=0.\Delta T < 0, W \neq 0$$

B
$$q=0,\, \Delta T = 0, W = 0$$

C
$$q =0, \Delta T\ne 0, W=0 $$

D
$$q\ne 0, \Delta T=0 , W=0 $$

Solution
Question 9
1 / -0

When an ideal diatomic gas is heated at constant pressure, the fraction of heat energy supplied which is used in doing work to maintain pressure constant is

A
$$5/7$$

B
$$7/2$$

C
$$2/7$$

D
$$2/5$$

Solution

$$\textbf{Step 1 - Heat energy required at constant pressure}$$
Total energy supplied to raise the temperature
of a diatomic gas at constant pressure,
$$Q = nC_{P}\triangle T$$ $$....(1)$$
Where $$C_{P}$$ is heat capacity at constant pressure
$$n$$ is number of moles
and $$\triangle T$$ is the temperature difference.

$$\textbf{Step 2 - Energy required for doing work}$$
We know
$$Q = \triangle u + w$$
$$w = Q - \triangle u$$
$$w = Q - nC_{V}\triangle T$$ $$....(2)$$
here $$C_{V}$$ is heat capacity at constant volume.
Put equation $$(1)$$ in $$(2)$$
$$w = nC_{P}\triangle T - nC_{V}\triangle T$$
$$w = n\triangle T(C_{P} - C_{V})$$
$$\Rightarrow w = n\triangle T\ R$$
$$[\because C_{P} - C_{V} = R]$$

$$\textbf{Step 3 - Fraction of heat energy supplied}$$
So, fraction of heat energy supplied whish is used in doing work
$$= \dfrac {w}{Q}$$
$$= \dfrac {nR\triangle T}{nC_{P}\triangle T}$$
$$= \dfrac {R}{C_{P}}$$
$$= \dfrac {R}{\dfrac {7}{5}R}$$ $$\textbf{[for distance ideal gas}$$ $$C_{P} = \dfrac {7}{5} R]$$
$$= \dfrac {5}{7}$$

Hence option (A) correct.
Question 10
1 / -0

A bullet of mass 100g moving with 20 m/s strikes a wooden plank and penetrates upto 20cm . Calculate the resistance offered by wooden plank

A
$$10^2 N$$

B
$$10^3N$$

C
$$10^4N$$

D
$$10^5 N$$

Solution

Given,
Mass of bullet$$=100g=10^{-1}m$$
Velocity of bullet $$V=20\dfrac{m}{s}$$
Distance travelled inside wood $$x=20cm=\dfrac{1}{5}m$$
Now , work done in stopping the bullet =kinetic energy of bullet
$$F×x=\dfrac{1}{2}mv^2$$
$$F=\dfrac{1}{2×0.2}×10^{-1}×{20}^2$$
$$F=10^2$$N

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Thermodynamics Test - 58

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Thermodynamics Test - 58

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Question 1

$$\dfrac{3R}{2}$$

$$\dfrac{11}{2}$$

$$\dfrac{5R}{2}$$

$$\dfrac{13}{2}$$

Solution

Question 2

$$4R$$

$$2.5R$$

$$3R$$

$$\dfrac{4R}{3}$$

Solution

Question 3

0.4

0.5

0.6

0.7

Solution

Question 4

Monoatomic

Diatomic

Polyatomic

Either a Monoatomic or Diatomic

Solution

Question 5

$$\sqrt{\dfrac{hc}{G}}$$

$$\sqrt{\dfrac{Gc}{h}}$$

$$\sqrt{\dfrac{hG}{c}}$$

$$\sqrt{hGc}$$

Solution

Question 6

always increase

always diminishes

remains constant

none of these

Solution

Question 7

$$2$$

$$\dfrac{3}{5}$$

$$\dfrac{3}{2}$$

$$\dfrac{4}{3}$$

Solution

Question 8

$$q=0.\Delta T < 0, W \neq 0$$

$$q=0,\, \Delta T = 0, W = 0$$

$$q =0, \Delta T\ne 0, W=0 $$

$$q\ne 0, \Delta T=0 , W=0 $$

Solution

Question 9

$$5/7$$

$$7/2$$

$$2/7$$

$$2/5$$

Solution

Question 10

A bullet of mass 100g moving with 20 m/s strikes a wooden plank and penetrates upto 20cm . Calculate the resistance offered by wooden plank

$$10^2 N$$

$$10^3N$$

$$10^4N$$

$$10^5 N$$

Solution

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