Tag: isothermal and adiabatic processes

Questions Related to isothermal and adiabatic processes

Consider a classroom that is roughly  $5 { m } \times 10  { m } \times 3  { m }.$  Initially   ${ t } = 20 ^ { \circ }  { C }$  and  $ { P } = 1$ atm. There are  $50$  people in an insulated class loosing energy to the room at the average rate of  $150$  watt per person. How long can they remain in class if the body temperature is  $37 ^ { \circ } \mathrm { C }$  and person feels uncomfortable above this temperature. Molar heat capacity of air  $= ( 7 / 2 ) R.$

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

  1. $4.34$ minutes

  2. $5.73$ minutes

  3. $6.86$ minutes

  4. $7.79$ minutes

Show answer
Correct Option: A

Some student find the value of $C _v$ and $C _P$ for two mole of  gas in calorie/gm -mol K.Which pair is most correct?

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

  1. $C _v=3, C _p=5$

  2. $C _v=3, C _p=6$

  3. $C _v=3, C _p=2$

  4. $C _v=3, C _p=4.2$

Show answer
Correct Option: A

Assertion : $C _P$ is always greater than $C _V$ in gases.
Reason : Work done at constant pressure is more than at constant volume.

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

  1. If both assertion and reason are true and reason is the correct explanation of assertion

  2. If both assertion and reason are true but reason is not the correct explanation of assertion

  3. If assertion is true but reason is false

  4. If both assertion and reason are false

Show answer
Correct Option: A

$C _{P}$ and $C _{V}$ are specific heats at constant pressure and constant volume, respectively. It is observed that $C _{P} - C _{V} = a$ for hydrogen gas $C _{P} - C _{V} = b$ for nitrogen gas. The correct relation between $a$ and $b$ is

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

  1. $a = b$

  2. $a = 14b$

  3. $a = 28b$

  4. $a = \dfrac {1}{14}b$

Show answer
Correct Option: B

If $C _{p} and C _{v}$ denoto the specific heats of nitron per unit mass at constant pressure and constant volume rest then 

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

  1. $C _{p} and C _{v}$=R/28

  2. $C _{p} and C _{v}$=R/14

  3. $C _{p} and C _{v}$=R

  4. $C _{p} and C _{v}$=28R

Show answer
Correct Option: A
Explanation:

According to Mayer's relation $C _{p}-C _{v}= R/m$

$C _{p}-C _{v}=\dfrac{R}{m}$
for nitrogen $m=28$
$ \therefore C _{p}- C _{v^{2}} R/28$

$C _v,$ respectively, If $\gamma =\dfrac { { C } _{ p } }{ { C } _{ v } } $ and $R$ is the universal gas constant, then $C _v$ is equal to 

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

  1. $\gamma ^R$

  2. $\dfrac{1+\gamma }{1-\gamma}$

  3. $\dfrac{R}{(\gamma-1)}$

  4. $\dfrac{(\gamma-1)}{R}$

Show answer
Correct Option: B

Each molecule of gas has f degree of freedom. The ratio $\dfrac { { C } _{ P } }{ { C } _{ V } } =\gamma $for the gas is 

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

  1. $1+\dfrac { f }{ 2 } $

  2. $1+\dfrac { 1 }{ f } $

  3. $1+\dfrac { 2 }{ f } $

  4. $\dfrac { f }{ 2 } $

Show answer
Correct Option: A

The molar specific heat at constant  pressure of an ideal gas is ( 7/2) R. the ratio of specific heat at constant pressure to that at constant volume is 

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

  1. 9/7

  2. 7/5

  3. 8/7

  4. 5/7

Show answer
Correct Option: A

Ration of $C _p$ and $C _v$ depends upon temperatures according to the following relation

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

  1. $\gamma \propto T$

  2. $\displaystyle \gamma \propto \frac{1}{T}$

  3. $\gamma \propto \sqrt{T}$

  4. $\gamma \propto T^o$

Show answer
Correct Option: D
Explanation:

$\gamma =\dfrac{C _p}{C _v}$ i.e, ratio of specific heat capacity at constant pressure and specific heat capacity at constant volume. It doesn't depend on temperature, i.e, it is independent of temperature.

Which type of ideal gas will have the largest value for $C _p-C _v?$

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

  1. Monoatomic

  2. Diatomic

  3. Polyatomic

  4. The value will be the same for all

Show answer
Correct Option: D