Thermodynamics Test

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Thermodynamics Test - 82

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Question 1
1 / -0

One mole of an ideal monatomic gas is taken along the path $$A B C A$$ as shown in the $$P V$$ diagram. The maximum temperature attained by the gas along the path $$B C$$ is given by:

A
$$\frac { 25 } { 4 } \frac { P _ { 0 } V _ { 0 } } { R }$$

B
$$\frac { 5 } { 8 } \frac { P _ { 0 } V _ { 0 } } { R }$$

C
$$\frac { 25 } { 8 } \frac { P _ { 0 } V _ { 0 } } { R }$$

D
$$\frac { 25 } { 16 } \frac { P _ { 0 } V _ { 0 } } { R }$$

Solution
Question 2
1 / -0

Which of the following integrals depends only on the initial and final states of a thermodynamic system (i.e., independent of the path of transformation)?

A
$$
\int P d V
$$

B
$$
\int d Q
$$

C
$$
\int T^2 d S
$$

D
none of these

Solution
Question 3
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The P-V diagrams of two difference masses $$m_1$$ and $$m_2$$ for an ideal gas at constant temperature $$T$$is given in the figure below.

A
$$m_1 = m_2$$

B
$$m_1 < m_2$$

C
$$m_1 > m_2$$

D
Data insufficient

Solution
Question 4
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Some of the thermodynamic parameters are state variables while some are process variables.Some grouping to the parameter are given.Choose the correct one.

A
State variables : Temperature,No of moles process variable : internal energy,work done by the the gas.

B
State variables ; Volume,Temperature process variables : Internal energy,work done by the gas.

C
State variables:Work done by the gas, heat rejected by the gas process variables: Temperature,volume.

D
State variables: internal energy,volume process variables: Work done by the gas,heat absorbed

Solution
Question 5
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A quantity of oxygen $$\left(\lambda=1.4\right)$$ is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored. The final pressure in terms of initial pressure $${P}_{1}$$ is

A
$$1.2{P}_{1}$$

B
$${P}_{1}$$

C
$$0.8{P}_{1}$$

D
$$0.5{P}_{1}$$

Solution
Question 6
1 / -0

10 gm of water is placed in a calorimeter of 100 gm water equivalent at $${10^0}$$. The heat required to raise the temperature of water to $${60^0}{\text{C}}$$ is:-

A
5000 cal

B
5500 cal

C
500 cal

D
4500 cal

Solution
Question 7
1 / -0

Two tanks $$A$$ and $$B$$ contain water at $$30 ^ { \circ } \mathrm { C }$$ and $$80 ^ { \circ } \mathrm { C }$$ respectively. Calculate the amount of water that must be taken from each tank to prepare $$40\mathrm { kg }$$ water at $$50 ^ { \circ } \mathrm { C } : -$$

A
$$24 \mathrm { kg } , 16 \mathrm { kg }$$

B
$$16 k g , 24 k g$$

C
$$20 \mathrm { kg } , 20 \mathrm { kg }$$

D
$$30 \mathrm { kg } , 10 \mathrm { kg }$$

Solution

Hint: According to Calorimetry principle heat gained by cooler body = heat losed by hotter body
Explanation:
Step-1: Find the relation between masses
Let $$m_{A} \& m_{B}$$ amount of water must be taken from tank $$\mathrm{A} \& \mathrm{~B}$$ Temperature of tank
Temperature of tank $$\mathrm{A}\left(T_{A}\right)=30^{\circ} \mathrm{C}$$
Temperature of tank B $$\left(T_{B}\right)=80^{\circ} \mathrm{C}$$
Temperature of mixture $$(T)=50^{\circ} \mathrm{C}$$
From principle of Calorimetry,
heat gained by cooler body $$=$$ heat losed by hotter body
where $$\mathrm{c}=$$ specific heat of water
$$\Rightarrow m_{A} \Delta T c=m_{B} \Delta T c \quad$$ where $$\mathrm{c}=$$ specific heat of water
$$\Rightarrow m_{A}\left(T-T_{A}\right)=m_{B}\left(T_{B}-T\right)$$
$$\Rightarrow m_{A}=\frac{T_{B}-T}{T-T_{A}} m_{B}$$
$$\Rightarrow m_{A}=\frac{80-50}{50-30} m_{B}=\frac{3}{2} m_{B}$$

Step-2: Find masses
Now, $$m_{A}+m_{B}=40$$
Putting the value from equation (1) we get,
$$\Rightarrow \frac{3}{2} m_{B}+m_{B}=40$$
$$\Rightarrow m_{B}=40 \times \frac{2}{5}=16$$
Hence, $$m_{A}=\frac{3}{2} \times 16=24$$
Therefore $$24 \mathrm{~kg}$$ and $$16 \mathrm{~kg}$$ water must be taken from tank $$\mathrm{A} \& \operatorname{tank} \mathrm{B}$$.
Question 8
1 / -0

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per 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
$$ T \propto \dfrac{1}{R} $$

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

C
$$ T \propto \mathbf{c}^{-R} $$

D
$$ T \propto e^{-3 R} $$

Solution
Question 9
1 / -0

The specific heat of a substance varies with temperature as $$s = 0.20 + 0.14\theta + 0.023{\theta ^2}(cal/g{m^ \circ }C)$$. Heat required top raise the temperature of $$2gm$$ of substance from $${5^ \circ }C$$ to $${10^ \circ }$$ is $${\theta}$$ is in $${^ \circ }C$$.

A
$$24cal$$

B
$$56cal$$

C
$$82cal$$

D
$$100cal$$

Solution
Question 10
1 / -0

The amount of heat required to raise the temperature of 100gm water from $$20^\circ C$$ to $$40^\circ C$$ will be-

A
$$100 \: calorie$$

B
$$2000 \: calorie$$

C
$$4000 \: calorie$$

D
$$0 \:calorie$$

Solution