Tag: heat and thermodynamics

Questions Related to heat and thermodynamics

A monoatomic gas expands at a constant pressure on heating. The percentage of heat supplied that increases the internal energy of the gas and that is involved in the expansion is 

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

  1. $75\%, 25\%$

  2. $25\%, 75\%$

  3. $60\%, 40\%$

  4. $40\%, 60\%$

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Correct Option: D
Explanation:

According to the first law of thermodynamics,
Q = U + W
Now, at constant pressure, 
W = $ P \Delta V = nR \Delta T $
U = $ n {C} _{v} \Delta T $
For, a monoatomic gas, $ {C} _{v} = 1.5 R $
Thus, Q = $ 2.5 nR \Delta T $
Now, $ \dfrac{U}{Q} = \dfrac{1.5R}{2.5R}  = 60 \%$
Similarly, $ \dfrac{W}{Q} = \dfrac{R}{2.5 R} = 40 \%$

If for hydrogen $C _p-C _v=m$ and for nitrogen $C _p-C _v=n$, where $C _p$ and $C _v$ refer to specific heats per unit mass respectively at constant pressure and constant volume, the relation between $m$ and $n$ is (molecular weight of hydrogen$=2$ and molecular weight of nitrogen$=14$)

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

  1. $n=14m$

  2. $n=7m$

  3. $m=7n$

  4. $m=14n$

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Correct Option: C
Explanation:

For hydrogen, $C _P-C _V=\dfrac{1}{M _{H _2}}\dfrac{dQ}{dT}=m$

For nitrogen, $C _P-C _V=\dfrac{1}{M _{N _2}}\dfrac{dQ}{dT}=n$
$\implies \dfrac{m}{n}=\dfrac{M _{N _2}}{M _{H _2}}=\dfrac{14}{2}=7$

The average degree of freedom per molecule for a gas are $6$. The gas performs $25 J$ of work when it expands at a constant pressure. The heat absorbed by gas is 

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

  1. $75 \ J$

  2. $100 \ J$

  3. $150\ J$

  4. $125 \ J$

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Correct Option: B
Explanation:

For a gas with 'n' degrees of freedom:
$\gamma = 1 + \dfrac{2}{n} = 1 + \dfrac{2}{6} = \dfrac{4}{3}$
$C _{p} = \dfrac{\gamma R}{\gamma - 1} = 4R$
$C _{v} = \dfrac{R}{\gamma - 1} = 3R$

Heat supplied for constant pressure process is $nC _{p}\Delta T$

Change in internal energy $nC _{v} \Delta T$
$\dfrac{\Delta U}{Q} = \dfrac{C _{v}}{C _{p}} = \dfrac{1}{\gamma} = \dfrac{3}{4}$

Hence $\dfrac{W}{Q} = 1 - \dfrac{\Delta U}{Q} = \dfrac{1}{4}$
$\dfrac{W}{Q}=1-\dfrac{3}{4}=\dfrac{1}{4}$
$\implies Q = 100J$

What is the ratio of specific heats of constant pressure and 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

A reversible adiabatic path on a P- V diagram foran ideal gas passes through state A where P = 0.7$\times $ ${ 10 }^{ 2  }$ N/${ m }^{ -2 }$ and v=0.0049 $ { m }^{ 3  }$, The ratio of specific heat of the gas is 1.4 , The slop of patch at A is:

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

  1. $2.0 \times{ 10 }^{ 3\quad }{ Nm }^{ -5 }$

  2. $1.0 \times{ 10 }^{ 3\quad }{ Nm }^{ -8}$

  3. $-2.0\times{ 10 }^{ 7\quad }{ Nm }^{ -3 }$

  4. $-1.0\times{ 10 }^{ 3\quad }{ Nm }^{ -5 }$

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Correct Option: A

The value of the ratio ${C} _{p}/{C} _{v}$ for hydrogen is $1.67$ a $30K$ but decreases to $1.4$ at $300K$ as more degrees of freedom become active. During this rise in temperature (assume H2 as ideal gas),

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

  1. ${C} _{p}$ remains constant but ${C} _{v}$ increases

  2. ${C} _{p}$ decreases but ${C} _{v}$ increases

  3. Both ${C} _{p}$ and ${C} _{v}$ decreases by the same amount

  4. Both ${C} _{p}$ and ${C} _{v}$ increase by the same amount

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Correct Option: C

A polyatomic gas with six degrees of freedom does $25\ J$ of work when it is expanded at constant pressure. The heat given to the gas is

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

  1. $100\ J$

  2. $150\ J$

  3. $200\ J$

  4. $250\ J$

Show answer
Correct Option: A
Explanation:

Degree of freedom, $f=6$
$\Rightarrow C _v=\dfrac{fR}{2}=3R$
$\Rightarrow C _p=C _v+R=4R$
Also work done $=\Delta W$=25J


Thus for isobaric process applying first law,
Heat given($\Delta Q$) $=$ internal energy change$(\Delta U)+\Delta W$
$\Rightarrow nC _p\Delta T=nC _v\Delta T+\Delta W$
$\Rightarrow 4nR\Delta T=3nR\Delta T +25J$
$\Rightarrow nR\Delta T=25J$
Hence, $ \Delta Q=4\times 25=100J$

A gas expands against a constant external pressure of  $2.00 atm, $ increasing its volume by $ 3.40 L.$   Simultaneously, the system absorbs  $400 J $ of heat from its surroundings. What is  $ \Delta E ,$  in joules, for this gas?

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

  1. $- 689$

  2. $-289$

  3. $+400$

  4. $+289$

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Correct Option: B

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

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

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Correct Option: A