Tag: the essence of change

Questions Related to the essence of change

a piece of lead falls from a height of $100m$ on a fixed non-conducting slab which brings it to rest. If the specific heat of lead is $30.6{\rm{ }}cal/kg{\,^ \circ }C,$, the increase in temperature of the slab immediately after collision is 

  1. ${6.72^ \circ }C$

  2. ${7.62^ \circ }C$

  3. ${5.62^ \circ }C$

  4. ${8.72^ \circ }C$


Correct Option: D

A metal ring of mass  2.1 kg and of 10 cm radius is revolving about its axis, Making 100/$\pi $ revoluation/s in the liquid is equal to 

  1. 100 cal

  2. 1000 cal

  3. 2100 cal

  4. 10 cal


Correct Option: A

The temperature inside and outside a refrigerator are $273\ K$ and $300\ K$ respectively Assuming that the refrigerator cycle is reversible, for every joule of work done, the heat delivered to the surrounding will be nearly

  1. $11\ J$

  2. $22\ J$

  3. $33\ J$

  4. $50\ J$


Correct Option: D

The height of the Niagara falls is $50$ metres, $(1 cal= 4.2 \mathrm\ { J }).$  Assume its mechanical energy can be completely converted into heat energy.

  1. Heat energy gained by each gram of water is $49 \times 10 ^ { 5 }\ \mathrm { cal }$

  2. Rise in temperature of water is $0.166^{ o }\ C/g$

  3. Rise in temperature of water is $0.12^{ o }\ C$

  4. Heal energy gained is $500\ joule/g$


Correct Option: C,D

The units of fore and length are made three times of their earlier values. Earlier the energy of a system was $81\ J$. What will be the energy of the same system in new units?

  1. $243$

  2. $729$

  3. $9$

  4. $None\ of\ the\ above$


Correct Option: B

When $1\ gm$. of water at $100^{\circ}C$ is converted into steam occupies $1671\ c.c.$ The amount of work done in converting water into steam is

  1. $167\ J$

  2. $180\ J$

  3. $184\ J$

  4. $2098\ J$


Correct Option: D

$1$ calorie is the heat required to increase the temperature of $1g$ of water by $1 ^ { \circ } \mathrm { C }$ from:

  1. $13.5 ^ { \circ } \mathrm { C } \text { to } 14.5 ^ { \circ } \mathrm { C } \text { at } 76 \mathrm { mm } \text { of } \mathrm { Hg }$

  2. $14.5 ^ { \circ } \mathrm { C } \text { to } 15.5 ^ { \circ } \mathrm { C } \text { at } 760 \mathrm { mm } \text { of } \mathrm { Hg }$

  3. $13.5 ^ { \circ } \mathrm { C } \text { to } 15.5 ^ { \circ } \mathrm { Cat } 76 \mathrm { mm } \text { of } \mathrm { Hg }$

  4. $15.5 ^ { \circ } \mathrm { C } \text { to } 16.5 ^ { \circ } \mathrm { C } \text { at } 700 \mathrm { mm } \text { of } \mathrm { Hg }$


Correct Option: A

If the amount of heat given to a system is $35\, J$ and the amount of work done on the system is $15\, J$, then the change in internal energy of the system is

  1. $- 50\, J$

  2. $20\, J$

  3. $30\, J$

  4. $50\, J$


Correct Option: D
Explanation:

Given,

$\Delta Q=+35J$
$\Delta W=-15J$
$\Delta U=?$
From law of thermodynamic,
$\Delta Q=\Delta U+\Delta W$
$\Delta U=\Delta Q-\Delta W$
$\Delta U=35-(-15)$
$\Delta U=35+15$
$\Delta U=50J$
The correct option is D. 

A geyser heats water flowing at the rate of 3.0 liters per minute from ${ 27 }^{ \circ  }C$ to ${ 77 }^{ \circ  }C$. If the geyser operates on a gas burner, the rate of consumption of the fuel if its heat of combustion is $4.0\times { 10 }^{ 4 }J/g$ per minute is

  1. $15.75g$

  2. $4 g$

  3. $0.3 g$

  4. $0.16 g$


Correct Option: A

A certain quantity of heat energy is given to a diatomic ideal gas which expands at constant pressure. The fraction of the heat energy that is converted into work is 

  1. $\dfrac 2 5$

  2. $\dfrac 2 7$

  3. $\dfrac 1 5$

  4. $\dfrac 5 7$


Correct Option: D
Explanation:

Supplied heat at constant pressure, 

$\Delta Q=nC _P \Delta T$
Change in internal energy,
$\Delta U=nC _V \Delta T$
ratio, $\dfrac{\Delta U}{\Delta Q}=\dfrac{nC _V \Delta T}{nC _P \Delta T}=\dfrac{C _V}{C _P}$. . . . . . . . .(1)
For diatomic ideal gas,
$C _P=\dfrac{7R}{2}\,  ,  C _V=\dfrac{5R}{2}$
From equation (1), we get
$\dfrac{\Delta U}{\Delta Q}=\dfrac{5R/2}{7R/2}=\dfrac{5}{7}$
$(5/7)^{th}$ part of heat supplied is used to increase internal energy.