Tag: heat energy transfers

Questions Related to heat energy transfers

How much heat energy in joules must be supplied to $14\ gms$ of nitrogen at room temperature to rise its temperature by $ 40^o C $ at constant pressure?
(Mol.wt.of $ N _2 = 28 gm , R = constant $)

physics heat energy transfers heat energy heat, internal energy and work internal energy

  1. $50R$

  2. $60R$

  3. $70R$

  4. $80R$

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Correct Option: C
Explanation:

Given,

Mass of nitrogen, $m=14gms$
Temperature, $T=40^0C$
Molecular weight of nitrogen, $M=28gms$
Now,
We know that,
Amount of heat supplied, $Q = n{C _p}\left( {dT} \right)$
No, of moles, $n = \frac{m}{M}$
$\therefore Q = \frac{m}{M}{C _p}dT$
$\begin{array}{l} =\frac { { 14 } }{ { 28 } } \times \frac { { 7R } }{ 2 } \times 40 \ =70R \end{array}$
Hence,
Option $C$ is correct answer.

Confined particles energy is given by 

physics heat energy transfers heat energy heat, internal energy and work internal energy

  1. $\dfrac{{{n^2}{h^2}}}{{2m{L^2}}}$

  2. $\dfrac{{2{n^2}{h^2}}}{{m{L^2}}}$

  3. $\dfrac{{{n^2}{h^2}}}{{8m{L^2}}}$

  4. $\dfrac{{{n^2}{h^2}}}{{4m{L^2}}}$

Show answer
Correct Option: C

At $3{ 0 }^{ \circ  }C$, a lead bullet of $50\ g$, is fired vertically upwards with a speed of $840\ m/s$. The specific heat of lead is $0.02\ cal/{ g }^{ \circ  }C$. on returning to the starting level, it strikes to a cake of ice at $0^{ \circ  }C$. Calculate the amount of ice melted (Assume all the energy is spent in melting only)

physics heat energy transfers heat energy heat, internal energy and work internal energy

  1. $62.7\ g$

  2. $55\ kg$

  3. $52.875\ kg$

  4. $52.875\ g$

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Correct Option: D
Explanation:
Kinetic energy of bullet = $\dfrac{mv^2}{2}$=$\dfrac12\times0.02\times840^2$ = $17640 joule =4200 cal$

heat supplied by lead to ice : $\Delta H _1 = ms\Delta T$ = $50\times 0.02 \times 30$ = $ 30 cal$

Total heat supplied = $4200 + 30 = 4230 cal$

let $M _{i}$ mass of ice melted $L$ is the latent heat of ice

$M _{i}L =4230$
$M _{i} \times 80 =4230$

$M _{i} =52.875 g$

A refrigerator has to transfer an average of $263J$ of heat per second from the temperature $-10^oC$ to $25^oC.$ The average power consumed, if no energy is lost is 

physics heat energy transfers heat energy heat, internal energy and work internal energy

  1. $100W$

  2. $7.5W$

  3. $25W$

  4. $35W$

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Correct Option: A

Hailstone at $0^{o}C$ falls from a height of $1\ km$ on an insulating surface converting whole of its kinetic energy into heat. What part of it will melt ? $(g=10\ m/s^{2}$)

physics heat energy transfers heat energy heat, internal energy and work internal energy

  1. $\dfrac{1}{33}$

  2. $\dfrac{1}{8}$

  3. $\dfrac{1}{33}\times 10^{-4}$

  4. All of it will melt

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Correct Option: A
Explanation:

Given:

The height from which the Hailstone falls is $1\ km$.

The energy lost by the hailstone is the potential energy and as it falls, this energy converts into heat energy. This heat energy is utilized in melting the hailstone.

So, the part of the hailstone melted is given by equating the potential energy to the latent heat of fusion.
$mgh=KmL$
$\because$ Latent heat of ice $=3.36\times 10^{5}J/kg$

$\Rightarrow K=\dfrac{gh}{L}$

$=\dfrac{10\times 1000}{3.36\times 10^{5}}$

$=\dfrac{1}{33}$

A block of mass $100\ g$ slides on a rough horizontal surface. If the speed of the block decreases from $10\ m/s^{-1}$ to $5\ m/s^{-1}$, the thermal energy developed in the process is:

physics heat energy transfers heat energy heat, internal energy and work internal energy

  1. $3.75\ J$

  2. $37.5\ J$

  3. $0.375\ J$

  4. $0.75\ J$

Show answer
Correct Option: A
Explanation:
Given:
The mass of the block is $100\ g$
The initial speed of the block is $10\ m/s$
The final speed of the block is $5\ m/s$

The thermal energy developed in the process is due to the lowering of the speed i.e. the reduction in the kinetic energy of the block.

Thermal energy = loss in kinetic energy
$=\dfrac{1}{2}m(v^2 _1-v^2 _2)$

$=\dfrac{1}{2}100\times 10^{-3}(10^2-5^2)$

$=3.75J$

Define the term heat :

physics heat energy transfers heat energy heat, internal energy and work internal energy

  1. the condition or quality of being hot

  2. the sensation of warmth or hotness

  3. the degree of hotness; temperature

  4. all of the above

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Correct Option: D
Explanation:

Heat is the transfer of kinetic energy from one medium or object to another. Such energy transfer can occur in three ways: radiation, conduction, and convection.

Also, it can be defined as the quality of being hot, high temperature, and degree of hotness and temperature.

In a sports meet the timing of a $200\ m$ straight dash is recorded at the finish point by starting an accurate stop watch on hearing the sound of starting gun fired at the starting point. The time recorded will be more accurate

physics heat energy transfers heat energy heat, internal energy and work internal energy

  1. In winter

  2. In summer

  3. In all seasons

  4. None of these

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Correct Option: B
Explanation:

The velocity of sound is directly proportional to the square root of absolute temperature.
The formula for velocity of sound in a gas is
$v = \sqrt {\dfrac {\gamma p}{\rho}}$
According to standard gas equation
$pV = RT$
or $p = \dfrac {RT}{V}$
$\therefore v = \sqrt {\dfrac {\gamma RT}{\rho \times V}} = \sqrt {\dfrac {\gamma RT}{M}}$
where $\rho \times V = M$, the molecular weight of the gas
$\therefore v\propto \sqrt {T}$
Hence, the sound of the gun fired at the starting point will reach the finishing point quicker in summer than in winter. The lapse of time due to the time taken by the sound in reaching the finish point will be less in summer and, hence the time recorded will be more accurate in summer than in winter.

Two blocks of steel A and B of the same shape and size, A being two times heavier than B, are at $40^{\circ}C$. The ratio of heat content of A to B is

physics heat energy transfers heat energy heat, internal energy and work internal energy

  1. $1$

  2. $4$

  3. $2$

  4. $\displaystyle\frac{1}{2}$

Show answer
Correct Option: C
Explanation:

The correct answer is option(C).

We know,
$Q=mC\Delta T$
Here Specific heat and raise in temperatures are equal.
And, given $2m _A=m _B$
So, the ratio of heat content can be,
$\dfrac {Q _1}{Q _2}=\dfrac {m _AC\Delta T}{m _BC\Delta T}=\dfrac {m _A}{m _B}=\dfrac 21=2$

State whether given statement is True or False
Heat is an invisible form of energy, which causes the sensation of hotness or coldness.

physics heat energy transfers heat energy heat, internal energy and work internal energy

  1. True

  2. False

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Correct Option: A
Explanation:

No body can see the exchange of heat or heat itself it is invisible and its effect or transfer can only be felt by the increases or decreases in temperature or the sensation of hotness and coldness.
Hence, OPTION : A (true).