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The value of R is used in most of the fundamental equations of thermodynamics, kinetic theory of gases, and so on. The value of R at atm, i.e. at standard atmospheric pressure is 8.3144598 J.
- The symbol ‘R’ is used to express the Gas constant.
- The gas constant is the molar equivalent of the Boltzmann constant, which is expressed in units of energy per unit temperature increment per unit amount of substance.
- The gas constant is also a combination of the constants from Boyle's law, Avogadro's law, Charles's law, and Gay-Lussac's law.
- The gas Constant is defined as the product of pressure and volume. It is also known as the ideal gas constant, universal gas constant, or molar constant.
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Key Terms: the value of R, ideal gas, atmospheric pressure, thermodynamics, kinetic theory of gases
NCERT Solutions of: Class 11 Physics Chapter 10 Mechanical Properties of Fluids
Gas constant
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The gas constant ‘R’ is defined as the work done by the gas (or on the gas) per unit mole per unit temperature change.
- The gas constant is also known as the ideal gas constant, universal gas constant, or molar constant.
- It is an important physical constant that is denoted by the letter ‘R’.
- Despite the fact that the ideal gas constant R is a constant, it can be expressed in a variety of unit systems.
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The gas constant R is defined as the product of Avogadro constant NA and Boltzmann constant k (or kB) and is given by
| R = NAk |
The value of R at standard atmospheric pressure (atm) is,
| R = 8.3144598 J.mol-1.K-1 |
Read More: Hooke’s Law
Formula of Gas Constant
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The value of R is calculated by using the ideal gas equation,
| PV = nRT |
On rearranging the equation, we get
| R = PV/nT |
Where
- R is the universal gas constant
- P denotes the ideal gas pressure.
- V denotes the ideal gas's volume.
- n is the number of moles.
- T is the Temperature
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Value of R
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The value of R can be expressed in a variety of unit systems depending on the necessity for calculation. For example, if we want to use the value of the gas constant in calories, we know that 4.184 joules = 1 calorie, so the value of R is
R = 8.31/4.184 Cal mol−1 K−1
Similarly, the value of the gas constant R can be expressed in a variety of units, as shown in the table below.
| Values of R | Units |
|---|---|
| 8.3144598 | J.K-1.mol-1 |
| 8.3144598 × 103 | amu.m2.s-2.K-1 |
| 8.3144598 × 10-2 | L.bar.K-1.mol-1 |
| 8.3144598 | m3.Pa.K-1.mol-1 |
| 62.363577 | L.Torr.K-1.mol-1 |
| 1.9872036 × 10-3 | kcal.K-1.mol-1 |
| 8.2057338 × 10-5 | m3.atm.K-1.mol-1 |
| 0.082057338 | L.atm.K-1.mol-1 |
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Things To Remember
- The gas constant ‘R’ is defined as the work done by the gas (or on the gas) per unit mole per unit temperature change.
- The value of R at standard atmospheric pressure (atm) is, R = 8.3144598 J.mol-1.K-1
- The value of R is calculated by rearranging the Ideal Gas Equation as- R = PV/nT
- The value of R will change as the pressure and volume of the system are adjusted.
- On the basis of the measuring system used, we can select the Value of R.
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Sample Questions
Ques: Define Gas Constant. (1 Mark)
Ans: Gas Constant is defined as the product of pressure and volume. It is also defined as the work done by the gas (or on the gas) per unit mole per unit temperature change.
Ques: How much is CP greater than Cv? (1 Mark)
Ans: CP is greater than Cv by universal gas constant ‘R’.
Ques: Determine the value of R in ergs mol1K1. (1 Mark)
Ans: We know that the value of R is 8.31 J mol1K1.
Now, instead of 1J = 107ergs, substitute 1J = 107ergs.
R = 8.31 x 107 ergs mol1K1.
So, the value of R under the CGS system is 8.31x107 ergs mol1k1.
Ques: Determine the value of R in L(atm) mol1K1. (1 Mark)
Ans: We know from the ideal gas equation that,
R = PV / nT
At STP,
n=1mol
P=1atm
T=273K
V=22.4L
Substituting the aforementioned values into the equation of R,
R = (1atm x 22.4 L)/(1mol x 243 K)
R = 0.0821 L (atm)mol-1K-1.
Ques: What is the relation between a Joule and a Calorie? (1 Mark)
Ans: The relation between Joule and Calories can be given as:
1 calorie = 4.184 joules.
Ques: What is the value of 1 Torr? Give the relation between Joule and Torr. (1 Mark)
Ans: Torr is a unit of atmospheric pressure equivalent to a pressure less than a 1mm column of Hg. The relation between Torr and Joule can be given as: 1L torr = 0.13332J.
Ques: Give the mathematical expression for the ideal gas equation. (1 Mark)
Ans: The mathematical expression for the ideal gas equation is:
PV = nRT
Where,
P= Pressure
V= Volume
n= no. of moles
T= Temperature
R is called the Gas constant.
Ques: Define gas constant. Write its other names and also give its value at atm. (2 Marks)
Ans: The gas constant ‘R’ is defined as the work done by the gas (or on the gas) per unit mole per unit temperature change. It is also known as the ideal gas constant, universal gas constant or the molar constant.
The ideal gas constant ‘R’ is a constant but its values vary as per the different unit systems. The value of R at standard atmospheric pressure (atm) is, R = 8.3144598 J.mol-1.K-1
Ques: Why do gases at high pressure and low temperature show a large deviation from ideal gas behavior? (2 Marks)
Ans: The intermolecular forces become appreciable when the temperature is low and pressure is high. Thus the volume occupied by the molecule is not negligibly small as compared to the volume of gas.
Ques: Why two holes are made in order to empty an oil tin? (2 marks)
Ans: Then the pressure inside the tin would be less than the atmospheric pressure if only one hole is made. So oil would not come out. If two holes are made, then the pressure inside the tin is equal to atmospheric pressure.
Ques: What is 105 Nm-2 pressure called? What is the value of 1 torr? (2 marks)
Ans: 105 Nm-2 pressure is called 1 bar. Torr is the unit of atmospheric pressure.
1 torr = 1 mm of Hg column
= 1.33 × 10-4 Nm-2
= 1.33 × 10-3dyne cm-2.
Ques: How can you check whether the barometer tube contains air or not? (1 mark)
Ans: The barometer tube is raised or lowered in a trough of mercury. If the height of the mercury column changes, then the barometric tube contains air.
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