Tag: principal and molar specific heats of gases

Questions Related to principal and molar specific heats of gases

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

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Correct Option: D

For an ideal gas

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

  1. $C _p$ is less than $C _v$

  2. $C _p$ is equal to $C _v$

  3. $C _p$ is greater than $C _v$

  4. $C _p=C _v=0$

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Correct Option: C
Explanation:

 For an ideal gas, $C _p$ is greater than $C _v$ because when gas is heated at constant volume, whole of the heat supplied is used to increase the temperature only but when gas is heated at constant pressure, the heat supplied is used to increases both temperature and the volume of gas (heat is used to do work)

The correct option is C.

Adiabatic exponent of a gas is equal to 

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

  1. $C _p\times C _v$

  2. $\dfrac{C _p}{C _v}$

  3. $C _p-C _v$

  4. $C _p+C _v$

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Correct Option: B

The molar specific heat capacity varies as $C=C _v + \beta V$ ($\beta$ is a constant). Then the equation of the process for an ideal gas is given as

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

  1. $T^{\frac{\beta}{RV} }= constant$

  2. $V^{\frac{\beta T}{R}}=constant$

  3. $T^{-\frac{R}{\beta V}}=constant$

  4. $V^{\frac{R}{\beta T}}=constant$

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Correct Option: B

$1$ $\mathrm { g }$ of a steam at $100 ^ { \circ } \mathrm { C }$ melts how much ice at $\mathrm { CC }$ (Latent heat of ice $= 80$ cal/gm and latent heat of steam $ = 540 \mathrm { cal/gm }$



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

  1. $1 gm$

  2. $2gm$

  3. $4 gm$

  4. $8 gm$

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Correct Option: D

The temperature of 5  mole of a gas which was held at constant volume was change from ${ 100 }^{ 0 }$ C to $120^{ 0 }$ C the change in internal energy was found to be 80 joules the total heat capacity of the gas at constant volume will be equal to 

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

  1. 8 J/K

  2. 0.8 J/K

  3. 4.0 J/K

  4. 0.4 J/K

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Correct Option: C

When $1\ mole$ of a monoatomic gas expands at constant pressure the ratio of the heat supplied that increases the internal energy of the gas and that used in expansion is

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

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

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

  3. $0$

  4. $\infty$

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Correct Option: B
Explanation:

Heat supplied to one mole of gas in a constant pressure process is given by: $Q = C _{p}\Delta T$
Change in the internal energy of gas is given by:$\Delta U = C _{v}\Delta T$


The ratio of heat that goes into increasing the internal energy is:
$\dfrac{\Delta U}{Q} = \dfrac{C _{v}}{C _{p}} = \dfrac{1}{\gamma}$

For a mono atomic gas $\gamma = \dfrac{5}{3}$
So, $\dfrac{3}{5}$ ratio of heat goes into increasing the internal energy, and the rest goes into expansion work = $\dfrac{2}{5}$ of heat supplied

Hence, the ratio of heat supplied to increase internal energy by heat supplied to do expansion is $ = \dfrac{3}{2}$

One mole of helium is heated at $0^o$C and constant pressure. How much heat is required to increase its volume threefold?

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

  1. $3820\ cal$

  2. $382\ cal$

  3. $38.2\ cal$

  4. $3.28\ cal$

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Correct Option: A
Explanation:

As it is a constant pressure process, using Charles law we get $\displaystyle\frac{V}{T}=constant$. Thus for a threefold increase in volume we get threefold increase in temperature. Thus we get the final temperature as $3(273)=819 K.$ Thus $\Delta T=819-273=546 K$.
Now as helium is a diatomic molecule, its degree of freedom f is 5. Ths we get $C _p$ for it as $(1+\displaystyle\frac{f}{2})R=(1+\frac{5}{2})R=\frac{7}{2}R$.
Thus heat transferred will be given as $\Delta Q=nC _p\Delta T$
or
$\Delta Q=1(\displaystyle\frac{7}{2})(1.987)(546)=3820\  cal$

When an ideal diatomic gas is heated at constant pressure then what fraction of heat given is used to increase internal energy of gas ? 

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

  1. $\dfrac{2}{5}$

  2. $\dfrac{3}{5}$

  3. $\dfrac{3}{7}$

  4. $\dfrac{5}{7}$

Show answer
Correct Option: D
Explanation:

For a diatomic gas we have the degree of freedom as 5. 

Thus heat given at constant pressure is given as $nC _p\Delta T=n(1+\displaystyle\dfrac{5}{2})R\Delta T=n\dfrac{7}{2}R\Delta T$. 
The heat given to change the internal energy is $nC _v\Delta T=n\displaystyle\dfrac{5}{2}R\Delta T$. 
The fraction of internal energy thus used is $\dfrac{5}{7}$ 

One mole of a monoatomic gas and one mole of a diatomic gas are mixed together. What is the molar specific heat at constant volume for the mixture ?

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

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

  2. $2 R$

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

  4. $3 R$

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Correct Option: B
Explanation:

$C _v$ is given as $\displaystyle\dfrac{f}{2}R$. Here $f$ is the degree of freedom. For monoatomic gas $f=3$ and for diatomic gas $f=5$. 

Thus we get $C _v$ for the mixture as $\displaystyle\dfrac{n _1}{n _1+n _2}(\dfrac{3}{2}R+\dfrac{5}{2}R)=2R$. Here $n _1$ and $n _2$ both are 1.