Option 4 : 10 ml of water at 20°C is mixed with 10 ml of sulphuric acid at 20°C

**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.Option 2 : 20°C

**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

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

\( \therefore \frac{{480}}{{24}} = 20\;^\circ C\)Option 1 : **\(\frac C{100}= \frac {F-32}{180}=\frac {R-492}{180}\)**

__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 –

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

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

Option 2 : Zeroth law of thermodynamics

**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.

Option 3 : at low pressure, the temperature of the gas is proportional of its pressure at constant volume

__Concept:__

A constant-volume gas thermometer is composed of a bulb that is attached to a mercury manometer. This thermometer operates on the principle of the Law of Gay-Lussac. The law states that when the temperature of an ideal gas increases, there is a corresponding increase in pressure. Also, when the temperature decreases, the pressure also decreases correspondingly.

A real gas behaves as an ideal gas at high temperature and low pressure. So, for a constant volume gas thermometer, one should fill the gas at high temperature and low pressure for better sensitivity of temperature measurement.

Option 2 : Radiation pyrometer

**Explanation:**

**The temperature of the sun is measured by using a radiation pyrometer.**- The main theory behind a radiation pyrometer is that the temperature is measured through the naturally emitted heat radiation by the body. This heat is known to be a function of its temperature
- The radiation pyrometer has an optical system including a lens, a mirror, and an adjustable eyepiece.
- The heat energy emitted from the hot body is passed on to the optical lens, which collects it and is focused on the detector with the help of the mirror and eyepiece arrangement.
- Thus, the heat energy is converted to its corresponding electrical signal by the detector and is sent to the output temperature display device.

Option 1 : 0^{th} law of Thermodynamics

__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.

For which of the following situations, zeroth law of thermodynamics will not be applicable?

Option 4 : 10 cc of water at 20°C is mixed with 10 cc of sulphuric acid at 20°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.

Option 1 : platinum resistance thermocouple

__Concept:__

Platinum resistance thermocouple:

- A platinum resistance thermometer also called PRT that determines the temperature by measuring the electrical resistance of a pure platinum wire.
- It works on the principle that the resistance of platinum changes with the change of temperature.
- This platinum wire acts as a temperature sensor and is very sensitive within the given range and has good reproducibility.
- With careful consideration, a wire of suitable length and diameter can be chosen so that the resistance of the device at 0° C is 100 Ω and such that the temperatures between ranges of -200°C to 1200°C can be detected.

∴ A platinum resistance thermocouple has a range between -200°C to 1200°C. Hence, option 1 is correct.

__Additional Information__

Resistance thermometers:

- Resistance of metallic conductors increases with temperature, while that of semiconductors generally decreases with temperature.
- Resistance thermometers employing metallic conductors for temperature measurement are called Resistance Temperature Detector (RTD), and those employing semiconductors are termed as Thermistors.
- RTDs are more rugged and have more or less linear characteristics over a wide temperature range.
- Thermistors have high-temperature sensitivity, but nonlinear characteristics.

The variation of resistance of metals with temperature is normally modeled in the form:

Rt = R0[1 + α(t - t0) + β(t - t0)2]

where Rt and R0 are the resistance values at t °C and t0 °C respectively and α, β are constants that depend on the metal.

- Copper, Nickel, and Platinum are mostly used as RTD materials.
- The range of temperature measurement is decided by the region, where the resistance-temperature characteristics are approximately linear.
- The resistance versus temperature characteristics of these materials is shown.
- Platinum has a linear range of operation up to 850°C, but it can detect between -200°C to 1200°C.
- While the useful range for Copper and Nickel are 120°C and 300°C respectively.

Statement (I): Negative temperatures are impossible on the Kelvin scale.

Statement (II): The Kelvin scale is thermodynamic temperature scales.Option 2 : Both Statement (I) and Statement (II) are individually true but statement (II) is not the correct explanation of Statement (I)

__Explanation:__

- Negative temperature are impossible on the Kelvin scale as the lowest value of temperature is zero kelvin (0 K) and according to thermodynamics, it is impossible to reach zero kelvin in finite number of stages.
- The
**Kelvin scale**is also called**thermodynamic temperature scale**as it has**no maximum temperature.**It can record temperature upto any level and also its lowest value is (zero kelvin) the temperature at which motion cease to exist and there is no possible value of temperature below it.

Statement (I): Thermometers using different thermometric property substance may give different readings except at two fixed points.

Statement (II): The thermodynamic temperature scale is independent of any particular thermometric substance.

Option 2 : Both Statements I) and Statement II) are individually true but Statement II) is not the correct explanation of Statement I)

**Explanation:**

- An absolute scale of temperature arises as a consequence of the Second law and that this thermodynamic scale is independent of any particular thermometric substance or property.
- Also, the temperature defined in this way enables us to introduce the useful concept of entropy. This theoretical scale is a good candidate for adoption as the ultimate standard.
**The thermometers are graded at two fixed points, for example, ice point and steam point of water, if two thermometers using two different thermometric properties are graded at these points then they are guaranteed to give the same reading at these fixed points.**- But they are not guaranteed to give the same reading between the graded points, because while calibrating it is assumed that there is linear variation in temperature with the thermometric property, but in the actual condition, the change in thermometric property may not follow this linearity.

**Therefore both the statements are individually true, statement l) is about the thermometric property and statement ll) is about the temperature scale. **

The basis for measuring a thermodynamic property of temperature is given by

Option 1 : Zeroth law of thermodynamics

__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.

- 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.

And to measure the direction of force we use term entropy which can be expressed as

\({\rm{\Delta }}S = \;\smallint \frac{{dQ}}{T}\)

ΔQ = heat exchange

ΔW = work done due to expansion

ΔU = internal energy of system

ΔS = change in entropy

T = temperature

__Explanation:__

From the above explanation, we can see that 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 as shown below.

This figure shows that when a body A is in thermal equilibrium with a body B, and also separately with a body C, then B and C will be in thermal equilibrium with each other.

This is the basis of temperature measurement and used to explain the concept of temperature.

__Tricks to remember:__

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

Option 1 : -2731.5

__Concept:__

**Absolute zero temperature: **The temperature at which the **enthalpy **and **entropy** of a gas reach their **minimum value** taken as** zero**. All the **particles stop moving** and all the **disorders disappear.**

The value of absolute zero temperature is **0K **or **-273.15°C**

**Celsius scale: **Celsius sale also called **centigrade scale** is based on **0°C **for the **freezing point **of water and **100°C ** for **boiling pint **for water.

**Methods of temperature measurement:**

**1)Two reference point system:**

In this method, two reference points are used

**Ice point (0°C) = T**_{i}**Steam point (100°C) = T**_{s}

****In this we consider the basic equation **T = a + b × X**

\({\bf{T}}\; = \;\frac{{ - 100 × {{\bf{X}}_{\bf{i}}}}}{{{{\bf{X}}_{\bf{s}}} - {{\bf{X}}_{\bf{i}}}}} + \;\frac{{100}}{{{{\bf{X}}_{\bf{s}}} - {{\bf{X}}_{\bf{i}}}}} × {\bf{X}}\)

where, **X _{i} = ice point **in new temperature scale,

**2) Single reference point system:**

In this method single reference points used i.e triple point of water **(273.15K)**

Here we consider the basic equation **T = a × X**

\({\bf{T}} = 273.15 \times \;\frac{{\bf{X}}}{{{{\bf{X}}_{{\bf{tp}}}}}}\)

where, **X =** **required temperature** on the new temperature scale, **X _{tp} = triple point temperature **on the new temperature scale

__Calculation:__

__Given:__

The freezing point of water **(X _{i}) = 0°X **and boiling point of water

The freezing point of water **(T _{i}) = 0°C **and boiling point of water

we know the basic equation for** two reference point system**

T = a + b × X .......(A)

Ti = a + b × Xi .......(1)

Ts = a + b × Xs .......(2)

substituting the above values in equation **1** and** 2**

0 = a + b × 0

100 = a + b × 1000

We get **a = 0 ** and ** b = 0.1, ** then substituting absolute zero temperature **(T) = -273.15 **and values of **a **and **b **in **equation A**

**T = a + b × X**

-273.15 = 0 + 0.1 × X

∴ **X = -2731.5°X ** ** **

__Important Points__

If **two thermometers** are agreed at ice point and steam point it does not mean that the intermediate temperature is also the same and all scales are arbitrary