Tag: isothermal and adiabatic processes

Questions Related to isothermal and adiabatic processes

Equal volumes of monoatomic and diatomic gases of same initial temperature and pressure are mixed. The ratio of the specific heats of the mixture ($C _p/C _v$) will be

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. $1.53$

  2. $1.52$

  3. $1.5$

  4. $1$

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Correct Option: C
Explanation:

$C _p$ for a gas is given as $(1+\displaystyle\dfrac{f}{2})R$ and $C _v$ is given as $\displaystyle\dfrac{f}{2}R$. Here f is the degree of freedom. 


For monoatomic gas it is 3 and for a diatomic gas it is 5. 

Thus, we get $C _p$ for the mixture as $\displaystyle\dfrac{5}{2}R+\dfrac{7}{2}R=6R$ and $C _v$ is given as $\displaystyle\dfrac{3}{2}R+\dfrac{5}{2}R=4R$.

Thus, the ratio $\displaystyle\dfrac{C _p}{C _v}$ is given as $\displaystyle\dfrac{3}{2}=1.5$

For an ideal gas during an adiabatic process $\left ( \frac{T^{1}}{P^{2}} \right )^{\frac{1}{5}}$  = constant.  The molar heat capacity at constant volume of the gas is 

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. 2.5 R

  2. 0.5 R

  3. 3 R

  4. $\frac{7}{2}R$

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Correct Option: A

Find the ratio of specific heat at constant pressure to the specific heat at constant volume for ${ NH } _{ 3 }$

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. 1.33

  2. 1.44

  3. 1.28

  4. 1.67

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Correct Option: C

An ideal gas has molar specific heat 5R/2 at constant pressure. If 300 J of heat is given to two moles of gas at constant pressure, the changes in temperature is : 

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. $ 7.22^oC$

  2. $8.94^oC$

  3. Zero

  4. $5^oC$

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Correct Option: D

The volume of 1 kg of hydrogen gas at N.T.P. is ${ 11.2 }m^{ 3 }$. Specific heat of hydrogen at constant volume is $100.46J\quad Kg^{ -1 }{ K }^{ -1 }$.Find the specific heat at constant pressure in $Jkg^{ -1 }{ K }^{ -1 }$?

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. 120.2

  2. 142.2

  3. 163.4

  4. 182.3

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Correct Option: A

The quantity of heat (in J) required to raise the temperature of $1.0\, kg$ of ethanol from $293.45\, K$ to the boiling point and then change the liquid to vapor at that temperature is closest to 
[Given : Boiling point of ethanol $351.45\, K$
              Specific heat capacity of liquid ethanol $2.44\, J\, g^{-1}\, K^{-1}$
               Latent heat of vaporization of ethanol $855\, J \, g^{-1}$]

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. $1.42\, \times 10^2$

  2. $9.97\, \times 10^2$

  3. $1.42\, \times 10^5$

  4. $9.97\, \times 10^5$

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Correct Option: D

A real gas behaves like an ideal gas at which pressure (P) nd temperature (T)?

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. low P,high T

  2. high P,high T

  3. low P ,low T

  4. high P, low T

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Correct Option: D

An ideal monatomic gas follows a law, $P\propto { T }^{ 2 }$ in addition to ideal gas law. Then molar heat capacity for the process is 

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. $R$

  2. $\dfrac { R }{ 2 } $

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

  4. $2R$

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Correct Option: A

An ideal gas expands into a vacuum in a rigid vessel. As a result there is :

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. a change in entropy

  2. a increase of pressure

  3. a change in temperature

  4. a decrease of internal energy

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Correct Option: B,C

Which of the following statements are incorrect?
I. If $Q > 0$, heat is added to the system.
II. If $W > 0$, work is done by the system.
III. If $W = 0$, work is done by the system.

principal and molar specific heats of gases isothermal and adiabatic processes specific heat capacity heat and thermodynamics physics

  1. II and III

  2. I, II and III

  3. I and II

  4. I and III

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Correct Option: A