Measurement of properties - class-XI

Yocto= $10^{-24}$,             Deca= $10^1$

The standard temperature is considered to be $273K$

The S.I unit of atmospheric pressure is $N/m^2$ or $Pascal$.

Luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle.

Mole is used to represent the amount of a substance. For an element or a compound, mole is given by

Room temperature is typically defined as approximately 20 to 25 degrees Celsius, which corresponds to roughly 293 to 298 Kelvin.

One fermi = $10^{-15}m = 10^{-13}cm$ .

The temperature of absolute zero is $T=t+273.15$

The SI unit for the coefficient of viscosity (dynamic viscosity) is the Pascal-second (Pa s). Since 1 Pascal = 1 N/m^2, the unit is (N/m^2) * s, which is N m^-2 s.

The question asks for the 'greatest of the combination', which refers to the uncertainty. The value with the largest absolute uncertainty (0.5) represents the least precise measurement.

1 meter = 100 cm. Therefore, 1 cubic meter = (100 cm)^3 = 1,000,000 cm^3, which is 10^6 cm^3.

SI unit of temperature is Kelvin because Kelvin was the the first person to suggest using Kelvin in thermodynamic temperature scale. 

$P _{dyne/cm^2}=P _{atm}\times 1.01325\times 10^6$

The SI unit of pressure is pascal. Newton is the unit of force and atm is not the S.I. unit of pressure.

The S.I unit of mass is kilogram (kg).

Our body temperature is maintained at $37^\circ C$ or $98^\circ F$ on an average. Our body has thermo-regulation mechanism that keeps the body at optimum operating temperature. Water plays an important role in this mechanism.

Force is the product of mass and acceleration

The S.I unit of volume is cubic meter $(m^3)$.

The SI unit of temperature is kelvin.

Water at $30^{\circ}C$ is liquid and it remains in liquid state from $0^{\circ}C$ to $100^{\circ}C$.

To convert from the Celsius scale to the Kelvin scale, we add $273$ to the Celsius scale. So, $-273+273=0\ K$

The S.I. unit of length is metre.

The atmospheric pressure at sea level is 1 atm.

The formula for conversion of centigrade unit to kelvin is :

Water boils at $100^{\circ}C$ and it converts into vapour above this temperature.

The S.I. unit of weight is newton since weight is the reaction force of an object due to gravity. 

To convert from Celsius scale to Kelvin scale, add 273 to Celsius scale.

$Density= \cfrac {mass}{volume}= \cfrac {15g}{2ml}= 7.5\quad g/ml$

Selected Prefixes and Their Meanin

$10^{-12}$ is called as pico.

SI unit of time is seconds.

Conversion factor involves same units. For example, length can be converted to length only, time to time only, etc.

Unit of Heat energy is joule ($J$) not kilopascals. kilopascal is unit for pressure.

We know that the 1 mL is equals to 0.001 L

J/Pa =  Work/Pressure =  Nm/Nm-2 = m3

Zero on the Celsius scale $(0^0C)$ is now defined as the equivalent to $273.15K$, with a temperature difference of $1^0C$ equivalent to a difference of $1K$, meaning the unit size in each scale is the same.

The prefix of ${ 10 }^{ -9 }=$ nano

The prefix of ${ 10 }^{ 3 }=$ kilo

The power required to do work by the application of force is energy.

$\text{Nuclear radii are measured in Fermi ie. }$$10^{-15}$

${ T } _{ K }={ (T } _{ F }+459.67)\times \frac { 5 }{ 9 } \ \Rightarrow 298={ (T } _{ F }+459.67)\times \frac { 5 }{ 9 } \ \Rightarrow \frac { 298\times 9 }{ 5 } -459.67={ T } _{ F }\ \Rightarrow { T } _{ F }=536.4-459.67={ 76.73 }^{ 0 }F$

The physical property of a body, substance or phenomenon that can be quantified by measurement is defined as a physical quantity.

The kilowatt-hour is commonly used as a billing unit for energy delivered to consumers by electric utilities.

Energy = Work done $(in\ Watt) =  Power\times time = Voltage \times current \times time$

Answer is option $B$. 

A. 1 atm = $1.01325 \times 10^5\ Pa$

Atomic radius is usually expressed in Angstrom units. It is because the size of atom is very small. It is equivalent to $1\times {10}^{-10}$metres.

One carat is equal to exactly $0.2$ grams.

Temperature differences are the same in both Celsius and Kelvin scales because the size of one degree Celsius is equal to the size of one Kelvin. Thus, T1 - T2 remains constant regardless of the scale used.

$100\ Tm=100000\ Gm$

$R$ is called as universal gas constant or molar gas constant.

Zepto = $10^{-21}m$ .

Solution:- (B) $\cfrac{9}{5} ℉$

The SI prefix 'femto' denotes a factor of 10^-15.

The relationship between Celsius and Fahrenheit is F = (9/5)C + 32. A change of 1 degree Celsius corresponds to a change of 9/5 degrees Fahrenheit.

Molality is defined as the number of moles of solute per kilogram of solvent, which has the units mol/kg or mol kg^-1.

Conversion from Fahrenheit to Celsius

Mass of a body is constant whereas weight of a body depends on the acceleration due to gravity at that point. Therefore, weight of body is not constant & varies from place to place.

The electron volt (symbol eV; also written electronvolt) is a unit of energy equal to approximately 1.602$\times$10$^{−19}$ joule (SI unit J). 

To convert from Kelvin scale to Celsius scale, subtract 273 from Celsius scale. 

Water at $-20^{\circ}C$ is ice so it is in solid state. It freezes at $0^{\circ}C$.

To convert from Kelvin scale to Celsius scale, subtract 273 from Kelvin scale, so $44-273=-229^oC$.

The temperature T in Kelvin (K) is equal to the temperature T in degrees Celsius $\displaystyle \left( ^{ \circ  }{ C } \right) + 273$: 

To convert from Celsius scale to Kelvin scale, we add 273 to Celsius scale. So, $30 + 273 = 303\ K$ 

We know,    $\boxed { {  }^{ 0 }C=\left( {  }^{ 0 }F-32 \right) \times \frac { 5 }{ 9 }  } $

Temperature in$ K$ = Temperature in $^{\circ}C + 273$

In the metric system, the prefix kilo-means $\displaystyle  10^3$. 
For example, 1 kg is equal to $\displaystyle  10^3 g$. 
1 km is equal to $\displaystyle  10^3 $ m.

Temperature after heating $= 58 + 20 = 78^0F$
Temperature in Kelvin $= (F -  32) \div 1.8 + 273$
                                    $= (78-32) \div 1.8 +273$
                                    $= 46 \div 1.8 + 273$
                                    $= 25.55 + 273$
                                    $= 298.5$ K

Metre $(m)$ is the basic unit of length in metric system.

SI unit of mass is Kilogram which is in MKS system.

milli- $\displaystyle  10^{-3}$
kilo- $\displaystyle  10^{3}$   
centi- $\displaystyle  10^{-2}$
micro- $\displaystyle  10^{-6}$
nano- $\displaystyle  10^{-9}$

Absolute zero, temperature at which a thermodynamic system has the lowest energy. It corresponds to $−273^oC$ $ ( 0 K)$.
Celsius scale is 273 greater in value than Kelvin scale.
$^0C = K - 273$

Solution:-

Boiling point is expressed in kelvin, molecular mass in kilograms, molarity in moles per litre, rate of reaction in moles per litre per second and density in grams per litre or milliltre.

0.5 mg of arsenic dissolved in 1 kg of solution. Both of the solute and solvent are given in terms of mass.

Zero on the Celsius scale $(0^0C)$ is now defined as the equivalent to $273.15K$, with a temperature difference of $1\ ^o C$ equivalent to a difference of $1\ K$, meaning the unit size in each scale is the same.

Thermometer that can measure rapidly changing temperature is thermocouple thermometer.
Advantages of a thermocouple thermometer:
(a) Easy to read by using a pointer or a digital display.
(b) Wide range of temperature $- 200^oC to 1600^oC$
(c) It has has a small thermal capacity and is used to measure rapidly changing temperatures.

Options A and B are incorrect. The Kelvin scale is the fundamental unit of the Temperature scale. It is defined as $\frac{ 1 }{ 273.16 }$ of the triple point (equilibrium among the solid, liquid, and gaseous phases) of pure water. Hence, option C is correct.

In Kelvin scale, temperature is expressed in Kelvin. In SI system, Kelvin is the unit of temperature. In this scale of temperature, zero of the scale corresponds to $-273^0C$, which is said to be the temperature at which the volume of a gas reduces to zero. Hence, $-273^0C$ is also known as the absolute zero. For the same reason, this scale of temperature is also known as absolute scale of temperature. On this scale, the lower fixed point i.e. the temperature of melting ice at normal pressure is +273K and the upper fixed point i.e. the temperature of boiling water at normal pressure is 373K. 

The SI units is based on seven base units. These are metre, kilogram, second, ampere, kelvin, mole and candela.

$E=mc^2$

$1\quad atm=1.01325\quad bar\approx 1\quad bar\neq 0.1\quad bar$

Units of physical quantities can be expressed in terms of fundamental units and such units are called $\text{derived units}$. 

Unit of area can be an example for derived unit. If $L$ is the length of the square then $L \times L$ is $L^{2}$ is its area. Hence, option A is correct.

                            	<span class="ng-binding">The units of fundamental physical quantities are called fundamental units. They are length, mass and time.<br>Hence option A is correct.<br></span>

Electrical unit     Single unit

(I) ampere-second                   coulomb

(II) volt-ampere                         Ampere

(III) volt-ampere$^{-1}$         Volt

(IV) walt/ampere ohm              Ohm

(V) joule / ampere second       Volt

So correct options are A- I B-III C-IV D-II E-V

Hence option A is correct.

Non-derived units or fundamental units are the units which are used to derive other units. The fundamental units are length, mass, temperature, time, electric current, liminous & mole.

Basic physical quantities are those that are physical fundamental units. There are seven basic fundamental quantities: Length, mass, time, electric current, amount of substance, luminous intensity & temperature. The quantities which are derived with the help of these basic physical quantities are called derived quantities. They are density, volume, pressure, force, etc.

Normally least count of burette is $ 0.10 cm^3$.

$1\ min=60\ s$

The Planck's constant is named after the physicist Max Planck. It links the frequency of the electromagnetic wave of a photon to its amount of energy.

Temperature is a measure of the average kinetic energy of the particles in a substance. 

Gas constant = $0.0821 $  $L atm K^{−1} mol^{−1}$

A barometer is a scientific instrument used in meteorology to measure atmospheric pressure. Pressure tendency can forecast short term changes in the weather. Numerous measurements of air pressure are used within surface weather analysis to help find surface troughs, high pressure systems and frontal boundaries.