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Introduction To Heat, Internal Energy And Work - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:35 AM | #JEE Main

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  • 42 Questions around this concept.

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A gas is compressed from a volume of \mathrm{2.0 \mathrm{~L}} to \mathrm{1.0 \mathrm{~L}} at a constant pressure of \mathrm{2.0 \mathrm{~atm}}. During the compression, the gas releases \mathrm{100 \mathrm{~J}} of heat to the surroundings. Calculate the work done by the gas.

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A gas confined within a piston-cylinder assembly undergoes a process where it expands at constant pressure of 2 \mathrm{~atm} from a volume of \mathrm{0.02 \mathrm{~m}^3\: to\: 0.04 \mathrm{~m}^3} During this process, 1500 \mathrm{~J} of heat is added to the gas. Calculate the work done by the gas and its change in internal energy.
 

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Carnot Cycle Efficiency

An ideal heat engine operates on a Carnot cycle between a hot reservoir at 800 \mathrm{~K} and a cold reservoir at 300 \mathrm{~K}. Calculate the efficiency of the engine.
 

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A piston-cylinder system contains 0.5 moles of an ideal gas initially at a pressure of 2 \mathrm{~atm} and a volume of 10 \mathrm{~L}.The gas undergoes an isothermal expansion at a constant temperature of 300 \mathrm{~K} until its volume doubles. Calculate the work done by the gas during the expansion and the amount of heat transferred.

Given:
          \text { Initial pressure }\left(P_{i}\right) =2 \mathrm{~atm}
          \text { Initial volume }\left(V_{i}\right) =10 \mathrm{~L}
          \text { Final volume }\left(V_{f}\right) =20 \mathrm{~L}
         \text { Number of moles }(n) =0.5 \mathrm{moles}
         \text { Gas constant }(R) =8.314 \mathrm{~J} /(\mathrm{mol} \mathrm{K})
          \text { Temperature }(T) =300 \mathrm{~K}

 

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A thermodynamic system undergoes a cyclic process that consists of two steps. In the first step, the system absorbs 500 \mathrm{~J} of heat and performs 300 \mathrm{~J}of work. In the second step, the system is brought back to its initial state by performing 200 \mathrm{~J} f work. Determine the heat exchanged during the second step.

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A refrigerator operates on a Carnot cycle between two reservoirs at temperatures \mathrm{T_{\text {hot }}=300 \mathrm{~K} \, \, and\, \, T_{\text {cold }}=200 \mathrm{~K}}. Calculate the coefficient of performance (COP) of the refrigerator.
 

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A container holds 0.2 \mathrm{~kg} of water initially at a temperature of 25^{\circ} \mathrm{C}. Heat is added to the water until its temperature reaches 100^{\circ} \mathrm{C}. Calculate the heat added to the water during this process.
Given the specific heat capacity of water is 4186 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}.
 

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A refrigerator operates on the reversed Carnot cycle. The cold reservoir temperature is 250 \mathrm{~K} and the hot reservoir temperature is 500 \mathrm{~K}. The refrigerator is used to cool an interior space to 275 \mathrm{~K}.Calculate the coefficient of performance (COP) of the refrigerator.
 

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A heat engine operates between a hot reservoir at a temperature of 500 K and a cold reservoir at a temperature
of 300 K. What is the maximum theoretical efficiency of this heat engine?

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An ideal gas undergoes a reversible isobaric process. The initial volume is 40 liters, the initial temperature is 300 \mathrm{~K}, and the final temperature is 400 \mathrm{~K}. Calculate the heat \mathrm{(Q)} added or removed from the gas during the process. Given the heat capacity at constant pressure \mathrm{\left(C_p\right)\: is \: 25 \mathrm{~J} / \mathrm{K}.}
 

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Concepts Covered - 2

Heat And Work

Heat 

Heat is the energy transfer due to the difference in temperature. Heat is a form of energy which the system can exchange with the surroundings if they are at different temperatures. The heat flows from higher temperature to lower temperature. 

Heat is expressed as 'q' 

Heat absorbed by the system = +q 

Heat evolved by the system = - q

 

Work 

It is the energy transfer due to the difference in pressure that is, the mode of energy transfer.


Types of work 

(i) Mechanical Work (Pressure volume work) = Force x Displacement 

(ii) Electrical Work = Potential difference x charge flow  , VQ = EnF

(iii) \mathrm{Expansion\ Work = P \times \Delta V = - P_{ext. } [ V _2-V _1] }

\textrm{P = external pressure And } \Delta \textrm{ V = increase or decrease in volume.}

(iv) Gravitational Work = mgh 

Here m = mass of body, 

g = acceleration due to gravity 

h = height moved.

 

Units: dyne cm or erg (C.G.S.) 

           Newton meter (joule) 

(i) If the gas expands, [V2> V1] and work is done by the system and W is negative. 

(ii) If the gas [V2 < V1] and work is done on the system and W is positive.


Different Types of Works and the Formulas 

(i) Work done in reversible isothermal process

\begin{array}{l}{\mathrm{W}=-2.303 \mathrm{nRT} \log _{10} \frac{\mathrm{V}_{2}}{\mathrm{V}_{1}}} \\ {\mathrm{W}=-2.303 \mathrm{nRT} \log _{10} \frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}}\end{array}

(ii) Work done in irreversible isothermal process

\\ \mathrm{ Work =- P_{ext. } ( V _2-V _1 )} \\ \mathrm{That \ is, \ Work =- P \times \Delta V }

Internal Energy

Internal Energy or Intrinsic Energy 

The energy stored within a substance is called its internal energy. The absolute value of internal energy cannot be determined. 

Or

It is the total energy of a substance depending upon its chemical nature, temperature, pressure, and volume, amount of substrate. It does not depend upon path in which the final state is achieved.

\begin{array}{l}{\mathrm{E}=\mathrm{E}_{\mathrm{t}}+\mathrm{E}_{\mathrm{r}}+\mathrm{E}_{\mathrm{v}}+\mathrm{E}_{\mathrm{e}}+\mathrm{E}_{\mathrm{n}}+\mathrm{E}_{\mathrm{PE}}+\mathrm{E}_{\mathrm{B}}} \\ {\mathrm{E}_{\mathrm{t}}=\text { Transitional energy }} \\ {\mathrm{E}_{\mathrm{r}}=\text { Rotational energy }} \\ {\mathrm{E}_{\mathrm{PE}}=\text { Potential energy }} \\ {\mathrm{E}_{\mathrm{B}}=\text { Bond energy }}\end{array}

The exact measurement of it is not possible so it is determined as  \mathrm {\Delta E} as follows:

\\ \Delta \mathrm{E}=\Sigma \mathrm{E}_{\mathrm{p}}-\Sigma \mathrm{E}_{\mathrm{R}} \\ {\Delta \mathrm{E}=\mathrm{E}_{\mathrm{f}}-\mathrm{E}_{\mathrm{i}}} \\ {\text {Here } \mathrm{E}_{\mathrm{f}}=\text { final internal energy }} \\ {\mathrm{Ei}=\text { Initial internal energy }} \\ {\mathrm{Ep}=\text { Internal energy of products }} \\ {\mathrm{Er}=\text { Internal energy of reactants }}

 

Facts about Internal Energy 

  • It is an extensive property.

  • Internal energy is a state property. 

  • The change in internal energy does not depend on the path by which the final state is reached.

  • Internal energy for an ideal gas is a function of temperature only so when the temperature is kept constant \mathrm{\Delta E}  is zero for an ideal gas.

\\\mathrm{E\propto T} \\ \\\mathrm{\Delta E = nC_v\Delta T [\ C_v \textup{ is the heat capacity at constant volume}]}

  • For a cyclic process \Delta \mathrm{E}  is zero. (E = state function), \mathrm { E \propto T}

  • For an ideal gas, it is totally kinetic energy as there is no molecular interaction. 

  • Internal energy for an ideal gas is a function of temperature only hence, when the temperature is kept constant it is zero.

  • At constant volume (Isochoric) \mathrm {Q_v= \Delta E}    

  • For exothermic process, \mathrm{\Delta E} is negative as but For endothermic process \mathrm{\Delta E} is positive as .

  • It is determined by using a Bomb calorimeter of the system.

\begin{array}{l}{\Delta \mathrm{E}=\frac{\mathrm{Z} \times \Delta \mathrm{T} \times \mathrm{m}}{\mathrm{W}}} \\ {\mathrm{Z}=\text { Heat capacity of Bomb calorimeter }} \\ {\Delta \mathrm{T}=\text { Rise in temperature }} \\ {\mathrm{w}=\text { Weight of substrate (amount) }} \\ {\mathrm{m}=\text { Molar mass of substrate }}\end{array}

Study it with Videos

Heat And Work
Internal Energy

Study other Related Concepts

Introduction To Heat, Internal Energy And Work Current Topic

Thermodynamics
Thermodynamic Property
State Functions
Reversible, Irreversible, Polytropic Process
Zeroth Law Of Thermodynamics
Introduction To Heat, Internal Energy And Work
Isothermal Expansion of an Ideal Gas
Graphical Comparison of Thermodynamic Processes
Heat Capacity - Relationship between Cp and Cv
Thermochemistry

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Books

Reference Books

Heat And Work

Chemistry Part I Textbook for Class XI

Page No. : 165

Line : 40

Internal Energy

Chemistry Part I Textbook for Class XI

Page No. : 162

Line : 25

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