Tag: specific heat capacity

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Questions Related to specific heat capacity

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

The amount of heat necessary to raise the temperature of $0.2 \ mol\ of\ N _2$ at constant pressure from $37^oC$ to $ 337^oC$  will be

  1. $746\ J$

  2. $1746\ J$

  3. $2746\ cal$

  4. $3746\ J$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$N _2$ is a diatomic molecule thus its degree of freedom is 5. Its $C _p$ is given as $(1+\displaystyle\dfrac{f}{2})R=(1+\dfrac{5}{2})R=\dfrac{7}{2}R$
Thus, we get the heat required as $Q=nC _p\Delta T=0.2\times \displaystyle\dfrac{7}{2}\times 8.314\times 300=1746  J$

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

The specific heat of a gas at constant pressure as compared to that at constant volume is

  1. less

  2. equal

  3. more

  4. constant
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When the gas is heated at constant pressure, some amount of heat is used up in increasing the volume of the gas. For a constant volume process no such heat is required. Thus $C _p>C _v$

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

The molar specific heat of an ideal gas at constant pressure and volume are $C _p$ and $C _v$ respectively. The value of $C _v$ is

  1. $R$

  2. $\gamma$ R

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

  4. $\dfrac{\gamma R}{\gamma-1}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We know that $\displaystyle\dfrac{C _p}{C _v}=\gamma$ and $C _p-C _v=R$.
Thus we get $C _v(\displaystyle\dfrac{C _p}{C _v}-1)=R$
or, $C _v=\displaystyle\dfrac{R}{\gamma -1}$

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

The gaseous mixture consists of $16\quad $ of helium and $16\quad $ of oxygen. The ratio $\cfrac { { C } _{ p } }{ { C } _{ v } } $ of the mixture is :-

  1. 1.59

  2. 1.62

  3. 1.4

  4. 1.54
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Helium is monatomic (gamma = 1.67) and Oxygen is diatomic (gamma = 1.4). Using the formula for the mixture ratio of specific heats, the result is approximately 1.62.

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

Calculate the specific heat of a gas at constant volume from the following data. Density of the gas at N.T.P =$19 \times 10 ^ { - 2 } \mathrm { kg } / \mathrm { m } ^ { 3 }$ $\left( C _ { p } / C _ { v } \right)$ = 1.4,J =$4.2 \times 10 ^ { 3 } \mathrm { J } / \mathrm { kcal }$ atmospheric pressure=$1.013 \times 10 ^ { 5 } N / m ^ { 2 }$ (in kcal /kg k)

  1. $2.162$

  2. $1.612$

  3. $1.192$

  4. $2.612$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the relationship Cp - Cv = R/M and Cp/Cv = gamma, we can solve for Cv using the density and pressure at NTP. The calculation yields approximately 2.162 kcal/kg K.

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

The ratio of the specific heat of air at constant pressure to its specific heat constant volume is

  1. Zero

  2. Greater than one

  3. Less than one

  4. Equal to one
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The correct answer is option(B).

The ratio of specific heat at constant pressure to the specific heat at constant volume is always greater than one.
As, when the gas is allowed to expand resulting in constant pressure, some of the heat is converted to work resulting in the need of a higher amount of heat to raise the temperature of the gas. Whereas when the volume of the gas is constant, the entire heat supplied is utilized in raising the gas temperature. Hence the heat required the raise the temperature of a unit mass of gas at constant pressure is greater than that required at constant volume. Hence the ratio $c _p:c _v$ is always greater than one.

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

Which of the following formula is wrong?

  1. $\displaystyle{C _{v} = \dfrac{R}{\gamma - 1}}$

  2. $\displaystyle{C _{p} = \dfrac{\gamma R}{\gamma - 1}}$

  3. $\displaystyle \dfrac{C _{p}}{ C _{v}} = \gamma$

  4. $C _{p} - C _{v} = 2R$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The different formula for specific heats is given by:

  • $\dfrac{C _{p}}{C _{v}} = \gamma$
  • $C _{p} - C _{v} = R$
Upon further simplification, we get:
  • $C _{p} = \dfrac{\gamma R}{\gamma -1}$
  • $C _{v} = \dfrac{R}{\gamma -1}$
The incorrect formula is
$C _{p} - C _{v} = 2R$
Hence option D is the answer.

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

For a gas the ratio of the two specific heats is $\dfrac{5}{3}$. If R $=$ 2 cal /mol-K then the values of $C _{p}$ and $C _{v}$ in cal / mol- K 

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

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

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

  4. $C _p=3 ,C _v=5 $
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

From given data we have $C _{p} - C _{v} = 2 $
and $\dfrac{C _{p}} { C _{v}} = \dfrac {5}{3} $
Solving both gives , 
$C _{p} = 5$ and  $ C _{v} = 3 $