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Assigning the basic dimensions to mass, length, time and temperature respectively as M, L, T and θ (Temperature), what are the dimensions of entropy?
- a)M LT-2 θ
- b)M L2 T-1 θ-1
- c)M L2 T-2θ-1
- d)M L3T-2 θ -1
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Assigning the basic dimensions to mass, length, time and temperature r...
dS=dQ/T
where,
Q= ML2T-2
T=θ
Most Upvoted Answer
Assigning the basic dimensions to mass, length, time and temperature r...
The dimensions of a physical quantity represent the fundamental units that are used to measure that quantity. In this case, we are asked to determine the dimensions of entropy, which is a thermodynamic property that represents the degree of disorder or randomness in a system.
Entropy is defined as the ratio of heat transfer to temperature, and it is denoted by the symbol S. To determine its dimensions, we can consider the equation for entropy:
S = Q/T
where S is entropy, Q is heat transfer, and T is temperature. By examining this equation, we can determine the dimensions of entropy based on the dimensions of heat transfer and temperature.
Heat transfer, Q, is typically measured in units of energy, which can be expressed as mass times length squared divided by time squared (ML^2/T^2). Therefore, the dimensions of heat transfer are [ML^2/T^2].
Temperature, T, is measured in units of temperature, which can be expressed as the dimensionless quantity [θ].
To determine the dimensions of entropy, we divide the dimensions of heat transfer by the dimensions of temperature:
[S] = [Q]/[T] = [ML^2/T^2]/[θ] = [ML^2/T^2θ]
Therefore, the dimensions of entropy are [M L^2 T^-2 θ^-1].
Among the given answer options, option 'C' (M L^2 T^-2 θ^-1) correctly represents the dimensions of entropy.
Entropy is defined as the ratio of heat transfer to temperature, and it is denoted by the symbol S. To determine its dimensions, we can consider the equation for entropy:
S = Q/T
where S is entropy, Q is heat transfer, and T is temperature. By examining this equation, we can determine the dimensions of entropy based on the dimensions of heat transfer and temperature.
Heat transfer, Q, is typically measured in units of energy, which can be expressed as mass times length squared divided by time squared (ML^2/T^2). Therefore, the dimensions of heat transfer are [ML^2/T^2].
Temperature, T, is measured in units of temperature, which can be expressed as the dimensionless quantity [θ].
To determine the dimensions of entropy, we divide the dimensions of heat transfer by the dimensions of temperature:
[S] = [Q]/[T] = [ML^2/T^2]/[θ] = [ML^2/T^2θ]
Therefore, the dimensions of entropy are [M L^2 T^-2 θ^-1].
Among the given answer options, option 'C' (M L^2 T^-2 θ^-1) correctly represents the dimensions of entropy.
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Assigning the basic dimensions to mass, length, time and temperature r...
To determine the dimensions of entropy, we start by recalling the definition of entropy in terms of heat transfer and temperature:
dS = δQ/T
Where dS is the differential entropy, δQ is the heat transferred, and T is the temperature.
The dimensional formula for heat (δQ) can be derived from its relation to energy. Energy (E) has dimensions of ML2T-2 (from the basic formula for kinetic energy ½mv2 or potential energy mgh).
Temperature (T) is assigned the dimension θ.
Using these, we can express the dimensions of dS as follows:
[dS] = [δQ/T] = ML2T-2/θ = M L2 T-2 θ-1
Thus, the dimensional formula for entropy is M L2 T-2 θ-1.
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