10th Science Unit 3 Thermal Physics Book Back Answers

The ideal gas equation is $PV = RT$, where $R$ is the universal gas constant.

The textbook gives its value as $8.31\,\mathrm{J\,mol^{-1}\,K^{-1}}$ (the value $1.38\times10^{-23}\,\mathrm{J\,K^{-1}}$ is Boltzmann's constant, not $R$).

One characteristic feature of heat transfer is that the mass of a system is not altered when it is heated or cooled.

Only the temperature, state or dimensions change; hence the change in mass is zero.

Linear expansion is the change in length of a body along one direction only, when its temperature changes.

So the expansion takes place along any one axis — either X or −X, or Y or −Y — that is, along (a) or (b).

The textbook defines temperature as the average kinetic energy (K.E) of the molecules of a substance (Section 3.1).

Total energy of a molecule, T.E = K.E + P.E, therefore K.E = T.E − P.E.

So temperature is the average difference in T.E and P.E of the molecules.

Option (b), the sum of P.E and K.E, is the total energy of the molecules, not the temperature.

Heat always flows from the body at higher temperature to the body at lower temperature.

Temperatures: A = 303 K, B = 304 K, C = 305 K, so A is the coldest and C is the hottest.

Therefore heat flows B → A (written A ← B), C → A (written A ← C) and C → B (written B ← C).

Avogadro's number ($N_A$) is the total number of atoms or molecules per mole of a substance.

Its value is $6.023 \times 10^{23}$ per mole.

Both temperature and heat have only magnitude and no direction.

Hence they are scalar quantities.

Calorie is a unit of heat energy defined for water.

One calorie raises the temperature of 1 gram of water through 1°C.

Boyle's law: $P \propto \dfrac{1}{V}$ at constant temperature.

So $P$ plotted against $\dfrac{1}{V}$ gives a straight line passing through the origin.

When a liquid in a container is heated, the container expands first, so the liquid level falls from $L_1$ to $L_2$, and on further heating rises to $L_3$.

Real expansion = $L_3 - L_2$ and apparent expansion = $L_3 - L_1$. Since $L_2 < L_1$, real expansion is the larger value.

Apparent expansion ignores the expansion of the container, so it is always less than the real expansion.

Heat energy flows because of a temperature difference between two bodies.

It always flows from the body at higher temperature to the body at lower temperature, until both attain the same temperature (thermal equilibrium).

This is one of the characteristic features of heat energy transfer given in the text.

Charles's law states that when the pressure of a gas is kept constant, the volume of the gas is directly proportional to its temperature.

That is, $V \propto T$ or $\dfrac{V}{T} =$ constant, not $V \propto \dfrac{1}{T}$.

Inverse proportionality between pressure and volume at constant temperature is Boyle's law, not Charles's law.

Linear expansion – when a body is heated, its length changes, so it matches change in length (d).

Superficial expansion – heating increases the area of the solid, so it matches change in area (e).

Cubical expansion – heating increases the volume of the solid, so it matches change in volume (a).

Heat transformation – heat always flows from a system at higher temperature to one at lower temperature, i.e. hot body to cold body (b).

Boltzmann constant – its value is $1.381 \times 10^{-23}\,\mathrm{JK^{-1}}$ (c).

Assertion check: when one end of a rod is heated, heat is conducted along the rod, so the other end also becomes hot. The assertion is true.

Reason check: heat always flows from a region of higher temperature to a region of lower temperature, not the other way. So the reason as stated is false.

Hence the assertion is true but the reason is false.

Assertion check: in gases the atoms/molecules are far apart, so gases are highly compressible compared with solids and liquids. True.

Reason check: the interatomic or intermolecular distance in a gas is comparatively large. True.

The large intermolecular distance is exactly why there is more free space to squeeze, so the reason correctly explains the assertion.

(Same idea as in the text: for a given rise in temperature a gas expands most, because its particles are forced further apart easily.)

Calorie is a unit of heat energy (other than the SI unit joule).

One calorie is the amount of heat energy required to raise the temperature of 1 gram of water through $1^\circ C$.

Related unit: one kilocalorie raises the temperature of 1 kilogram of water through $1^\circ C$.

Linear expansion: when a body is heated or cooled, the change is in the length of the body. It is also called longitudinal expansion; $\dfrac{\Delta L}{L_o}=\alpha_L \Delta T$.

Superficial (areal) expansion: the increase is in the area of the solid due to heating; $\dfrac{\Delta A}{A_o}=\alpha_A \Delta T$.

Linear expansion is measured by the coefficient of linear expansion $\alpha_L$, superficial expansion by the coefficient of superficial expansion $\alpha_A$; both have the SI unit $K^{-1}$.

When a solid is heated its volume increases; this is cubical or volumetric expansion.

The ratio of increase in volume of the body per degree rise in temperature to its unit volume is called the coefficient of cubical expansion.

It is given by $\dfrac{\Delta V}{V_o}=\alpha_V \Delta T$ and its SI unit is $K^{-1}$. Its value differs for different materials.

Boyle's law: when the temperature of a gas is kept constant, the volume of a fixed mass of gas is inversely proportional to its pressure.

In symbols, $P \propto \dfrac{1}{V}$.

Hence for an invariable mass of a perfect gas at constant temperature, $PV =$ constant.

The law of volume is Charles's law, formulated by the French scientist Jacques Charles.

It states that when the pressure of a gas is kept constant, the volume of the gas is directly proportional to its temperature.

In symbols, $V \propto T$ or $\dfrac{V}{T}=$ constant.

Real gas: the molecules or atoms interact with each other with a definite amount of intermolecular or interatomic force of attraction.

Ideal gas: the atoms or molecules do not interact with each other; it is also called a perfect gas.

In practice no gas is ideal; every gas has some interaction among its molecules.

At very high temperature or low pressure the forces of attraction become weak, so a real gas behaves as an ideal gas. Ideal gases obey Boyle's law, Charles's law and Avogadro's law.

If a liquid is heated directly without using any container, the expansion observed is the real expansion of the liquid.

The coefficient of real expansion is the ratio of the true rise in volume of the liquid per degree rise in temperature to its unit volume.

Its SI unit is $K^{-1}$.

A liquid is always heated in a container, so part of the heat expands the container and part expands the liquid.

The expansion of a liquid observed without considering the expansion of the container is the apparent expansion.

The coefficient of apparent expansion is the ratio of the apparent rise in volume of the liquid per degree rise in temperature to its unit volume; SI unit $K^{-1}$.

Real expansion is always greater than apparent expansion.

Given: original area $A_o = 10\,\mathrm{m^2}$, final area $= 11\,\mathrm{m^2}$, so change in area $\Delta A = 11 - 10 = 1\,\mathrm{m^2}$; initial temperature $T_1 = 90\,\mathrm{K}$; coefficient of superficial expansion $\alpha_A = 0.0021\,\mathrm{K^{-1}}$.

Formula for superficial (areal) expansion: $\dfrac{\Delta A}{A_o} = \alpha_A \Delta T$, so $\Delta T = \dfrac{\Delta A}{A_o \, \alpha_A}$.

Substituting: $\Delta T = \dfrac{1}{10 \times 0.0021} = \dfrac{1}{0.021}$.

Rise in temperature: $\Delta T = 47.6\,\mathrm{K}$.

Final temperature $T_2 = T_1 + \Delta T = 90 + 47.6 = 137.6\,\mathrm{K}$.

The printed data mean the volume of the zinc bar increases from $0.25\,\mathrm{m^3}$ to $0.3\,\mathrm{m^3}$ (an increase, as stated), for a temperature change $\Delta T = 50\,\mathrm{K}$.

Original volume $V_o = 0.25\,\mathrm{m^3}$; change in volume $\Delta V = 0.3 - 0.25 = 0.05\,\mathrm{m^3}$.

Formula for cubical expansion: $\dfrac{\Delta V}{V_o} = \alpha_V \,\Delta T$, hence $\alpha_V = \dfrac{\Delta V}{V_o\,\Delta T}$.

Substituting: $\alpha_V = \dfrac{0.05}{0.25 \times 50} = \dfrac{0.05}{12.5} = 0.004\,\mathrm{K^{-1}}$.

So $\alpha_V = 4 \times 10^{-3}\,\mathrm{K^{-1}}$.

Both ice and water are at the same temperature, $0^\circ\mathrm{C}$, but the hand holding the ice feels more chillness.

Heat always flows from the body at higher temperature (your hand, about $37^\circ\mathrm{C}$) to the body at lower temperature ($0^\circ\mathrm{C}$) until thermal equilibrium is reached.

The ice must first absorb a large amount of heat energy (latent heat) from your hand to change its state from solid to liquid, and this happens without any rise in its temperature.

So the hand with ice loses much more heat energy than the hand with water at the same temperature, and hence feels colder.