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Assertion (A): Thermal diffusivity is a dimensionless quantity.
Reason (R): In M-L-T-Q system the dimensions of thermal diffusivityare [L2T-1]
- a)Both A and R are individually true and R is the correct explanation of A
- b)Both A and R are individually true but R is not the correct explanation of A
- c)A is true but R is false
- d)A is false but R is true
Correct answer is option 'D'. Can you explain this answer?
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Assertion (A): Thermal diffusivity is a dimensionless quantity.Reason ...
The units of thermal diffusivity is m^2/s. it is thermal conductivity/(density*specific heat at const P). hence has dimensions.
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Assertion (A): Thermal diffusivity is a dimensionless quantity.Reason ...
Assertion (A): Thermal diffusivity is a dimensionless quantity.
Reason (R): In M-L-T-Q system, the dimensions of thermal diffusivity are [L2T-1].
The correct answer is option 'D', which states that Assertion (A) is false but Reason (R) is true.
Explanation:
Thermal Diffusivity:
Thermal diffusivity is a property that describes how quickly heat diffuses through a material. It is defined as the ratio of the material's thermal conductivity to its volumetric heat capacity.
Mathematically, thermal diffusivity (α) is given by the formula:
α = k / (ρ * Cp)
Where:
α = Thermal diffusivity
k = Thermal conductivity
ρ = Density
Cp = Specific heat capacity at constant pressure
Assertion (A): Thermal diffusivity is a dimensionless quantity:
Thermal diffusivity is not a dimensionless quantity. It has dimensions of [L2T-1] in the M-L-T-Q system. The dimensions of thermal diffusivity are derived from the dimensions of thermal conductivity (k), density (ρ), and specific heat capacity (Cp). Therefore, Assertion (A) is false.
Reason (R): In M-L-T-Q system, the dimensions of thermal diffusivity are [L2T-1]:
The dimensions of thermal diffusivity are [L2T-1] in the M-L-T-Q system. This can be derived by substituting the dimensions of thermal conductivity (k), density (ρ), and specific heat capacity (Cp) into the formula for thermal diffusivity (α). The dimensions of thermal conductivity are [MLT-3K-1], the dimensions of density are [ML-3], and the dimensions of specific heat capacity are [L2T-2K-1]. When these dimensions are divided, the resulting dimensions for thermal diffusivity are [L2T-1]. Therefore, Reason (R) is true.
In conclusion, Assertion (A) is false because thermal diffusivity is not a dimensionless quantity. Reason (R) is true because the dimensions of thermal diffusivity are [L2T-1] in the M-L-T-Q system.
Reason (R): In M-L-T-Q system, the dimensions of thermal diffusivity are [L2T-1].
The correct answer is option 'D', which states that Assertion (A) is false but Reason (R) is true.
Explanation:
Thermal Diffusivity:
Thermal diffusivity is a property that describes how quickly heat diffuses through a material. It is defined as the ratio of the material's thermal conductivity to its volumetric heat capacity.
Mathematically, thermal diffusivity (α) is given by the formula:
α = k / (ρ * Cp)
Where:
α = Thermal diffusivity
k = Thermal conductivity
ρ = Density
Cp = Specific heat capacity at constant pressure
Assertion (A): Thermal diffusivity is a dimensionless quantity:
Thermal diffusivity is not a dimensionless quantity. It has dimensions of [L2T-1] in the M-L-T-Q system. The dimensions of thermal diffusivity are derived from the dimensions of thermal conductivity (k), density (ρ), and specific heat capacity (Cp). Therefore, Assertion (A) is false.
Reason (R): In M-L-T-Q system, the dimensions of thermal diffusivity are [L2T-1]:
The dimensions of thermal diffusivity are [L2T-1] in the M-L-T-Q system. This can be derived by substituting the dimensions of thermal conductivity (k), density (ρ), and specific heat capacity (Cp) into the formula for thermal diffusivity (α). The dimensions of thermal conductivity are [MLT-3K-1], the dimensions of density are [ML-3], and the dimensions of specific heat capacity are [L2T-2K-1]. When these dimensions are divided, the resulting dimensions for thermal diffusivity are [L2T-1]. Therefore, Reason (R) is true.
In conclusion, Assertion (A) is false because thermal diffusivity is not a dimensionless quantity. Reason (R) is true because the dimensions of thermal diffusivity are [L2T-1] in the M-L-T-Q system.
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Assertion (A): Thermal diffusivity is a dimensionless quantity.Reason (R): In M-L-T-Q system the dimensions of thermal diffusivityare [L2T-1] a)Both A and R are individually true and R is the correct explanation of Ab)Both A and R are individually true but R is not the correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'D'. Can you explain this answer?
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ample number of questions to practice Assertion (A): Thermal diffusivity is a dimensionless quantity.Reason (R): In M-L-T-Q system the dimensions of thermal diffusivityare [L2T-1] a)Both A and R are individually true and R is the correct explanation of Ab)Both A and R are individually true but R is not the correct explanation of Ac)A is true but R is falsed)A is false but R is trueCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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