physics : class11 Dimensions of Thermal Quantities : Dimensions of Physical Quantities : Physical World and Measurement MCQ Questions and Answers
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Dimensions of Thermal Quantities
MCQ questions and answers.
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MCQ Questions
1. The dimensional formula of specific heat capacity is:
A.
[M L^2 T^-2 Θ^-1]
B.
[M^0 L^2 T^-2 Θ^-1]
C.
[M^0 L^2 T^-1 Θ^-1]
D.
[M L T^-2 Θ^-1]
Correct Answer:
[M^0 L^2 T^-2 Θ^-1]
Explanation:
Specific heat capacity is heat supplied per unit mass per unit temperature rise. Since heat has dimensions [M L^2 T^-2], its dimensions are [M L^2 T^-2]/[M Θ] = [M^0 L^2 T^-2 Θ^-1].
2. A material has thermal conductivity k, specific heat capacity c, and density ρ. The dimensional formula of the thermal diffusivity k/(ρc) is:
A.
[L^2 T^-1]
B.
[L T^-1 Θ^-1]
C.
[L^2 T^-2 Θ^-1]
D.
[M^-1 L^3 T^-1]
Correct Answer:
[L^2 T^-1]
Explanation:
Thermal conductivity has dimensions [M L T^-3 Θ^-1], while ρc has dimensions [M L^-3] [L^2 T^-2 Θ^-1] = [M L^-1 T^-2 Θ^-1]. Their ratio is [L^2 T^-1].
3. The coefficient of linear expansion α is related to the change in length ΔL and temperature change ΔΘ by ΔL = αLΔΘ. Its dimensional formula is:
A.
[L Θ^-1]
B.
[Θ^-1]
C.
[L^-1 Θ]
D.
[L^0 Θ]
Correct Answer:
[Θ^-1]
Explanation:
From α = ΔL/(LΔΘ), both ΔL and L have dimension L, so they cancel. Therefore, α has dimension Θ^-1.
4. The dimensions of the universal gas constant R, using the relation PV = nRΘ, are:
A.
[M L^2 T^-2 Θ^-1 mol^-1]
B.
[M L T^-2 Θ^-1 mol^-1]
C.
[M L^2 T^-1 Θ^-1 mol^-1]
D.
[M^0 L^2 T^-2 Θ^-1 mol^-1]
Correct Answer:
[M L^2 T^-2 Θ^-1 mol^-1]
Explanation:
From PV = nRΘ, R = PV/(nΘ). Pressure times volume has dimensions [M L^-1 T^-2][L^3] = [M L^2 T^-2]. Dividing by amount of substance and temperature gives [M L^2 T^-2 Θ^-1 mol^-1].
5. The dimensional formula of thermal conductivity k, defined through the heat-flow relation Q/t = kA(ΔΘ/l), is:
A.
[M L T^-3 Θ^-1]
B.
[M L^2 T^-3 Θ^-1]
C.
[M L^-1 T^-3 Θ^-1]
D.
[M L T^-2 Θ^-1]
Correct Answer:
[M L T^-3 Θ^-1]
Explanation:
The dimensions of heat-flow rate Q/t are [M L^2 T^-3]. Since k = (Q/t)l/(AΔΘ), its dimensions are [M L^2 T^-3][L]/[L^2 Θ] = [M L T^-3 Θ^-1].
6. A quantity X is defined by X = k/(ρcα), where k is thermal conductivity, ρ is density, c is specific heat capacity, and α is the coefficient of linear expansion. The dimensions of X are:
A.
[L^2 T^-1]
B.
[L^2 T^-1 Θ]
C.
[L^2 T^-1 Θ^-1]
D.
[L T^-1 Θ]
Correct Answer:
[L^2 T^-1 Θ]
Explanation:
The dimensions of k/(ρc) are [L^2 T^-1], which are the dimensions of thermal diffusivity. Dividing further by α, whose dimensions are [Θ^-1], multiplies the result by Θ, giving [L^2 T^-1 Θ].
7. The latent heat L of a substance is defined by Q = mL. Its dimensional formula is:
A.
[M L^2 T^-2]
B.
[L^2 T^-2]
C.
[M L^2 T^-2 Θ^-1]
D.
[M^0 L^2 T^-1]
Correct Answer:
[L^2 T^-2]
Explanation:
Latent heat is heat supplied per unit mass. Since heat has dimensions [M L^2 T^-2], dividing by mass gives [L^2 T^-2]. Unlike specific heat, latent heat does not involve an explicit temperature interval.
8. The dimensional formula of entropy, defined thermodynamically by dS = dQ/Θ for a reversible process, is:
A.
[M L^2 T^-2 Θ^-1]
B.
[M L^2 T^-2 Θ]
C.
[M L T^-2 Θ^-1]
D.
[M^0 L^2 T^-2 Θ^-1]
Correct Answer:
[M L^2 T^-2 Θ^-1]
Explanation:
Entropy is heat divided by thermodynamic temperature. Therefore, its dimensions are [M L^2 T^-2]/[Θ] = [M L^2 T^-2 Θ^-1].
9. For a solid, the heat required for a temperature rise is Q = mcΔΘ. If Q, m, and ΔΘ are measured in dimensions [M L^2 T^-2], [M], and [Θ], respectively, the dimensions of c are:
10. The quantity β = (1/V)(ΔV/ΔΘ) represents the coefficient of cubical expansion. Its dimensional formula is:
A.
[L^-1 Θ^-1]
B.
[Θ^-1]
C.
[L^3 Θ^-1]
D.
[L^-3 Θ]
Correct Answer:
[Θ^-1]
Explanation:
The change in volume ΔV and the original volume V have the same dimensions, so their ratio is dimensionless. Dividing by temperature change ΔΘ gives β the dimensions Θ^-1.
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