Zeroth Law of Thermodynamics MCQ Quiz - Objective Question with Answer for Zeroth Law of Thermodynamics - Download Free PDF

Explanation:

Zeroth Law of Thermodynamics

• The Zeroth Law of Thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This law provides a fundamental basis for the concept of temperature.

Working Principle: The Zeroth Law essentially implies that temperature is a fundamental and measurable property of matter. If system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then system A and system B must be in thermal equilibrium with each other. This logical reasoning allows for the establishment of temperature as a transitive property.

Significance in Measurement of Temperature: The Zeroth Law is crucial because it allows for the creation of temperature scales and the use of thermometers. It enables us to compare temperatures of different systems and ensures that thermometers can provide consistent and reliable temperature readings.

Applications: The principles of the Zeroth Law are applied in various fields, including:

• Thermometry: The development and calibration of thermometers rely on the Zeroth Law, ensuring accurate temperature measurement.
• Engineering: Temperature control and monitoring in processes such as heating, cooling, and chemical reactions are based on the Zeroth Law.
• Scientific Research: Accurate temperature measurement is essential in experiments and studies involving thermal properties of materials and systems.

The question involves the concept of applying a correction to a measured value to determine the true value of the temperature. When a thermometer is calibrated, a correction factor is often provided to account for any systematic error in its readings. In this case, the thermometer reading is 80.5ºC, and the correction from the calibration curve is -0.25ºC. To find the true value of the temperature, the correction factor must be added to the measured temperature. This can be expressed mathematically as: $$T_{\text{true}} = T_{\text{measured}} + T_{\text{correction}}$$ Where: - Ttrue" id="MathJax-Element-447-Frame" role="presentation" style="position: relative;" tabindex="0">TtrueTtrue $T_{\text{true}}$ is the true temperature. - Tmeasured" id="MathJax-Element-448-Frame" role="presentation" style="position: relative;" tabindex="0">TmeasuredTmeasured $T_{\text{measured}}$ is the temperature measured by the thermometer. - Tcorrection" id="MathJax-Element-449-Frame" role="presentation" style="position: relative;" tabindex="0">TcorrectionTcorrection $T_{\text{correction}}$ is the correction factor from the calibration curve. Given: - Tmeasured=80.5∘C" id="MathJax-Element-450-Frame" role="presentation" style="position: relative;" tabindex="0">Tmeasured=80.5∘CTmeasured=80.5∘C $T_{\text{measured}} = 80.5\,^\circ\text{C}$ - Tcorrection=−0.25∘C" id="MathJax-Element-451-Frame" role="presentation" style="position: relative;" tabindex="0">Tcorrection=−0.25∘CTcorrection=−0.25∘C $T_{\text{correction}} = -0.25\,^\circ\text{C}$ We substitute these values into the formula: $$T_{\text{true}} = 80.5\,^\circ\text{C} + (-0.25\,^\circ\text{C}) = 80.5\,^\circ\text{C} - 0.25\,^\circ\text{C} = 80.25\,^\circ\text{C}$$ Therefore, the true value of the temperature is 80.25ºC, which corresponds to Option 3 in the given choices.

Explanation:

The zeroth law of thermodynamics states that if two thermodynamic systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

A thermometer works on the principle of Zeroth's law of Thermodynamics.

A thermometer is based on the principle of finding the temperature by measuring the thermometric property.

Points to remember

• The first law of thermodynamics states that energy can neither be created nor destroyed in an isolated system. The first law measures internal energy.
• The second law of thermodynamics states that the entropy of an isolated system always increases. the second law measures entropy.
• According to the Third law of thermodynamics, when the temperature of a perfect crystal is equal to absolute 0 (0 K), the entropy of the crystal is 0.

Important Points

Kirchhoff's law:

It states that the emissivity (ϵ) of the surface of a body is equal to its absorptivity (α) when the body is in thermal equilibrium with its surroundings.

ϵ = α.

Concept:

• The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

This law is the basis for the temperature measurement.

Additional Information

• The first law of thermodynamics states that energy cannot be created or destroyed in an isolated system; energy can only be transferred or changed from one form to another.

The first law of thermodynamics is a restatement of the law of conservation of energy

i.e., According to the first law of Thermodynamics:

ΔQ = ΔW + ΔU

• Now the First Law of Thermodynamics helped us in understanding the principle of conservation of energy, whereas according to the Second Law of thermodynamics for natural system heat always flows in one direction (higher temperature to lower temperature body) unless it aided by an external factor.

The correct answer is 0ºC

Explanation:

The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

This law is the basis for the temperature measurement.

• By replacing the third body with a thermometer, the Zeroth law can be restated as two bodies are in thermal equilibrium if both have the same temperature reading even if they are not in contact.
• The thermometer is based on the principle of finding the temperature by measuring the thermometric property.

Explanation:

Celsius scale 

• In this scale, LFP (ice point) is taken 0° and UFP (steam point) is taken 100°.
• The temperature measured on this scale all in degree Celsius (° C).

Fahrenheit scale 

• This scale of temperature has LFP as 32° F and UFP as 212° F .
• The change in temperature of 1° F corresponds to a change of less than 1° on the Celsius scale.

Kelvin scale 

• The Kelvin temperature scale is also known as the thermodynamic scale. The triple point of water is also selected to be the zero of the scale of temperature.
• The temperatures measured on this scale are in Kelvin (K).

Rankine scale

• This scale of temperature has LPF as 492° R and UFP as 672° R.
• Interval of this scale is according to Fahrenheit.
• The temperature measured on this scale are in Rankine (R)

 

All these temperatures are related to each other by the following relationship

\(\frac C{100}= \frac {F-32}{180}=\frac {R-492}{180}= \frac {K -273}{100}\)

Additional Information

Relationship between the Celsius and Fahrenheit scale is –

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

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

Explanation:

According to Zeroth Law, if system A is in thermal equilibrium with system C, and system B is thermal equilibrium with systems C, then system A is in thermal equilibrium with system B.

Now, two systems are said to be in (mutual) thermal equilibrium if, when they are placed in thermal contact (basically, contact that permits the exchange of energy between them), their state variables do not change.

In case of mixing of water and sulphuric acid, the enormous amount of heat is released as mixing is highly exothermic. So there is no more any thermal equilibrium. So Zeroth Law is not valid.

Explanation:

Temperature: It is the measure of the degree of hotness and coldness of a body. The SI unit of temperature is Kelvin (K).

The major temperature scales are:

• Celsius scale: It is also known as the centigrade scale, and most commonly used scale. It is defined from assigning 0° C to 100° C of freezing and boiling point of water at 1 atmospheric pressure.
• Fahrenheit scale: The temperature scale which is based on 32° for the freezing point of water and 212° for the boiling point of water and the interval between the two range divided into 180 equal parts is called Degree Fahrenheit scale.
• Kelvin scale: It is the base unit of temperature, denoted with K. There are no negative numbers on the Kelvin scale as the lowest is 0 K.

The relation between Celsius and Kelvin is:

°C + 273.15 = K

The relation between degree Fahrenheit and degree Celsius is given by:

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

Kelvin scale is an absolute scale and it is also known as the absolute thermodynamic scale.

Before 1954 temperature scales were based on two reference points. e.g. Degree Celsius and Fahrenheit scale.

After 1954 the scale and temperature measurement has been based on a single reference point. i.e the Tripple point of water is used as a single reference point.

According to the internationally accepted convention \(1K = ({1\over273.16})\) th of the triple point of water.

Concept:

Temperature is always a linear function of the thermometric property i.e.

T = ax + b

where x is the thermometric property.

Calculation:

Given:

T = ax + b, here the length of the column is the thermometric property.

At melting Ice temp T = 0°C, x = 10 mm.

0 = 10a + b                           (i)

At steam, T = 100°C, x = 250 mm.

100 = 250a + b                    (ii)

From (i) and (ii)

\(a = \frac{{100}}{{240}} = \frac{{10}}{{24}}\)

\(b = - 10a = \frac{{ - 100}}{{24}}\)

Now, for Tap water, at x = 58 m

\({\rm{T}} = 58{\rm{a}} + {\rm{b}} = \frac{{58 \times 10}}{{24}} - \frac{{100}}{{24}}\)

\( \therefore \frac{{480}}{{24}} = 20\;^\circ C\)

Concept:

Zeroth Law of thermodynamics:

• The zeroth law of thermodynamics states that if two bodies are each in thermal equilibrium with a third one, then they are in thermal equilibrium with each other.
• Systems are said to be in thermal equilibrium if there is no heat transfer, even if they are in a position to transfer heat, based on other factors.

​Explanation:

Option 1

50 cc of water at 25°C is mixed with 150 cc of water at 25°C 

Water with different quantities (50 cc and 150 cc) are in thermal equilibrium (At 25°C), Hence the zeroth law of thermodynamics will be applicable.

Option 2

500 cc of milk at 15°C is mixed with 100 cc of water at 15°C

Milk and water at 15°C are at thermal equilibrium. Hence the zeroth law of thermodynamics will be applicable.

Option 3

5 kg of wet stream at 100°C is mixed with 50 kg of dry and saturated steam at 100°C

wet steam and dry and saturated steam are at 100°C. They form a pure substance and don't participate in the reaction. Hence they are in thermal equilibrium.

Option 4

In 10 cc of water at 20°C is mixed with 10 cc of sulphuric acid at 20°C there is no thermal equilibrium between the components of the mixture because there will be a spontaneous ionic reaction which highly exothermic in nature.

Explanation:

Thermocouple:

• The thermocouple is a sensor used to measure temperature.
• It consists of two dissimilar electrical conductors forming a junction. 
• Nichrome contains 80% Ni and 20% Cr. It is used mostly in thermocouples and in strain gauges.
• A thermocouple produces a temperature-dependent voltage as a result of the thermoelectric effect and this voltage can be interpreted to measure temperature.
• Thermocouples are typically selected because of their low cost, high-temperature limits, wide temperature ranges, and durable nature.
• Thermocouple gives the fastest response in less time.
• Thermocouples are less accurate than RTDs in the low-temperature range. 
• When compared with RTDs the durability of the Thermocouple is more.
• The typical range of temperature of the thermocouple is -1800C to 23200C.​

Concept:

Temperature is always a linear function of the thermometric property i.e.

T = ax + b

where x is the thermometric property.

Calculation:

Given:

t = ap + b, here p is the thermometric property.

At Ice point t = 0 °C, p = 2 bar.

0 = 2a + b     ....(1)

At steam point t = 100 °C, p = 4 bar.

100 = 4a + b   ....(2)

Solving (1) and (2)

a = 50 and b = -100

∴ t = 50p -100

At p = 3.5 bar

t = 50p -100

t = (50 × 3.5) - 100 = 75 °C.

Explanation:

The zeroth law of thermodynamics states that if two thermodynamic systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.

A thermometer works on the principle of Zeroth's law of Thermodynamics.

A thermometer is based on the principle of finding the temperature by measuring the thermometric property.

Points to remember

• The first law of thermodynamics states that energy can neither be created nor destroyed in an isolated system. The first law measures internal energy.
• The second law of thermodynamics states that the entropy of an isolated system always increases. the second law measures entropy.
• According to the Third law of thermodynamics, when the temperature of a perfect crystal is equal to absolute 0 (0 K), the entropy of the crystal is 0.

Important Points

Kirchhoff's law:

It states that the emissivity (ϵ) of the surface of a body is equal to its absorptivity (α) when the body is in thermal equilibrium with its surroundings.

ϵ = α.

Explanation:

Zeroth law of thermodynamics:

• The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.
• This law is the basis for temperature measurement.

First law of thermodynamics:

• The first law of thermodynamics states that energy cannot be created or destroyed in an isolated system; energy can only be transferred or changed from one form to another.

The first law of thermodynamics is a restatement of the law of conservation of energy

i.e., According to the first law of Thermodynamics:

ΔQ = ΔW + ΔU

• Now the First Law of Thermodynamics helped us in understanding the principle of conservation of energy, whereas according to the Second Law of thermodynamics for natural systems heat always flows in one direction (higher temperature to lower temperature body) unless it is aided by an external factor.

Second law of thermodynamics:

The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

• In other words- The second law of thermodynamics states that the total entropy of an isolated system always increases over time, or remains constant in ideal cases where the system is in a steady state or undergoing a reversible process. This increase in entropy accounts for the irreversibility of natural processes. 
• Entropy is a measure of disturbance, the higher the entropy with the positive sign, the more are the chances of the reaction taking place spontaneously. The SI unit of Entropy is Joule per Kelvin (J/K).
• The second law gives the definition of entropy term.

ΔS = ΔQ/T

Where Δ S is entropy change, Δ Q is energy change and T is temperature

Third law of thermodynamics: 

• As the temperature approaches absolute zero, the entropy of a system/crystal approaches a constant minimum.

ΔST at 0 K = 0

where ΔS = change in entropy 

Shortcut Trick

This is the conclusive point for all three laws of thermodynamics.

• Zeroth law: Concept of temperature
• First law: Concept of internal energy/ energy conservation
• Second law: Concept of entropy/ heat flow