Solution-Class 8-Science-Chapter-14-Measurement and Effect of Heat-Maharashtra Board

False. - The temperature of a substance is measured in °C or °F or K.

True

True

False. – Generally objects expand on heating. There are some exceptions to this.

False - Atoms of a solid are bound to each other due to the forces acting between them.

False -The average kinetic energy of atoms in a hot object is greater than the average kinetic energy of atoms in a cold object.

a. A thermometer is used to measure temperature.

b. The apparatus used to measure heat is called a calorimeter.

c. Temperature is the measures of the averagekinetic energy of the atoms in a substance.

d. The heat contained in a substance is the measures of the totalkinetic energy of atoms in the substance.

Shivani's tea will be prepared first, because in a given time, the amount of heat received by the vessel on a stove is far greater than that received by the vessel kept in a solar cooker.

Thus, the time taken by the tea to reach its boiling point will be less than Nishigandha’s vessel. Hence, Shivani's tea will be ready first than Nishigandha’s  tea.

Figure shows a clinical thermometer. As the body temperature of a healthy person is 37 ⁰C, clinical thermometers are designed to measure temperatures between 35 ⁰C and 42 ⁰C. (or from 95°F to 108°F)

• A clinical thermometer has a narrow stem and a long bulb filled with mercury (or alcohol).  Long bulb and thin stem, increases the sensitivity of the thermometer.
• There is a small constriction in the stem above the bulb.
• When the bulb of the thermometer is held in the armpit or the mouth of a patient, the mercury (or alcohol) in the bulb rises in the stem.
• When it is taken out of the patient’s body, the small constriction does not allow the mercury (or alcohol) from the stem to retreat into the bulb. Thus, this arrangement enables us to read the temperature of the patient’s body at ease after the removal of the thermometer from his body.
• There is a red arrow mark which indicates the temperature of a healthy person.
• The surface of the stem is in the form of a magnifying -glass and hence it enables us to see the thin thread of mercury clearly.

The thermometer used in a laboratory has wider range and does not have constriction like a clinical thermometer.

Calorimeter : A calorimeter is used to measure the heat content of an object.

Using this equipment, we can measure the heat produced or absorbed in a physical or chemical process.

A calorimeter is shown in figure

• Similar to a thermosflask, a calorimeter has two vessels, an inner and an outer one.
• The inner vessel is made of copper. The inner vessel is thermally isolated from the surroundings. This way, no heat can be transferred from the inner to the outer vessel or from the outer to the inner vessel.
• The outer vessel is made of wood and is covered with a heat resistant lid. The lid has two holes, one for the thermometer and the other for the stirrer.
• A thermometer for measuring the temperature and a stirrer for stirring the liquid in the calorimeter are fitted in it.
• The inner and outer surfaces of the inner vessel are polished for minimizing exchange of heat with the surroundings by radiation. A heat resistant ring covers the inner vessel.

All solids expand on heating. As rails are made up of steel, these also expand in summers and contract in winters. Also, they expand due to rise in temperature caused by the friction between the rails and the wheels of the running train. These expansion and contraction can cause sagging and bending of rails which could derail the trains running on them. Thus, the rails have been provided with gaps at specific distance so as to prevent this bending of rails. These spaces get closer in summers and wider in winters.

Expansion coefficients of liquid : When a liquid which is held in a container is heated, both the container and the liquid expand. The expansion of the container is usually very small compared to that of the liquid in it. Often, it can be ignored.

Suppose, a liquid is heated so that its temperature rises by ΔT (very small) and its volume increases from V₁ to V₂.

Experimentally, it is found that the increase in volume, V₂ — V₁, is proportional to V₁ and DT.

Hence, V₂ — V_{1 ∝}  V₁ ΔT.

∴ V₂ — V₁ = β V₁ ΔT, Where, b is a constant of proportionality called the volumetric expansion coefficient of the liquid.

β = \(\frac{V_2-V_1}{V_1ΔT}\)  It is expressed in per °C.

We have V₂ = V₁ + βV_1ΔT = V₁(1 + βΔT)

β is the increase in the volume of a liquid per unit original volume per unit rise in its temperature.

Expansion coefficients of gas : A gas is enclosed in a container. When it is heated at constant pressure, both the container and the gas expand.

Suppose a gas is heated at constant Pressure so that its temperature rises by ΔT

(Very Small) and its volume increases from DT (very small) and its volume increases from V₁ to V₂.

Experimentally, it is found that the increase in volume, V₂ — V₁, is proportional to V₁ and ΔT.

Hence, V₂ — V_{1 ∝}  V₁ ΔT

∴ V₂ — V₁ = β V₁ ΔT Where, b is a constant of proportionality, the volumetric expansion coefficient, called the constant pressure expansion coefficient.

β = \(\frac{V_2-V_1}{V_1ΔT}\)  It is expressed in per °C.

We have V₂ = V₁ + βV_1ΔT = V₁(1 + βΔT)

β is the increase in the volume of a gas per unit original volume per unit rise in its temperature when the pressure is kept constant.

Given : F = 2C, ∴ C = F/2, F= ?

We know

\(\frac{F-32}{9}=\frac{C}{5}\)

∴ \(\frac{F-32}{9}=\frac{F/2}{5}\)

∴ F−32 = \frac{9F}{2×5}\)

∴ F – 0.9F = 32, ∴ 0.1 F =32

∴ F = 32/0.1 = 320 ⁰F

l₁ = 20 m, l₂ – l₁ = 0.4 cm = 4 x 10^-3 m, T_i = 18 °C, λ for iron = 11.5 x 10^-6/°C

l₂ – l₁ = λl₁ΔT

∴ ΔT = \(\frac{l_2-l_1}{ λl_1}=\frac{4×10^{-3}}{11.5×10^{-6}×20}=\frac{400}{23}\) = 17.39 °C

Now ΔT = T_f – T_{i , ∴} T_f  = ΔT + T_i  = 17.39 + 18 = 35.39 °C

The bridge will be in good shape upto 35.39 °C

Given :  ΔT= 30 °C – 15 °C = 15 °C, l₁ = 324 m,  λ for iron = 11.5 x 10^–6/°C

l₂ – l₁ = λl₁ΔT 

∴ l₂ – l₁ = 11.5 x 10^–6 x 324 x 15

= 55890 x 10^–6 m

= 55890 x 10^–4 cm

= 5.589 cm (nearly 5.6-cm)

This is the increase in the length, i.e., the increase in the height of Eiffel Tower.

Given : c_A = c , c_B = 2c, Q_A = Q, Q_B = 4Q ΔT= same, m_A = m, m_B = ?

We know Q = mcΔT

∴ΔT = Q/mc

As ΔT is same for substance A and B

∴ \(\frac{Q_A}{m_Ac_A}=\frac{Q_B}{m_Bc_B}\)

∴ \(\frac{Q}{mc}=\frac{4Q}{m_B2c}\)

∴ m_B = 2m This is the mass of B

Given : m = 3kg, = 3000 g, Q = 600 cal, ΔT = 10 ⁰C, c = ?

We know Q = mcΔT

∴ c = Q/mΔT = 600/(3000 x 10) = 0.02 cal/g ⁰C

This is the specific heat of substance