Physics, asked by wwwdebbarmaayush923, 10 months ago

Derive the dimension of specific heat.

Answers

Answered by sridevigarapati00821

Answer:

The specific heat capacity of a substance is the heat capacity of a sample of the substance divided by the mass of the sample. Informally, it is the amount of energy that must be added, in the form of heat, to one unit of mass of the substance in order to cause an increase of one unit in its temperature. The SI unit of specific heat is joule per kelvin and kilogram, J/(K kg).[1][2] For example, at a temperature of 25 °C (the specific heat capacity can vary with the temperature), the heat required to raise the temperature of 1 kg of water by 1 K (equivalent to 1 °C) is 4179.6 joules, meaning that the specific heat of water is 4179.6 J·kg−1·K−1.[3]

The specific heat often varies with temperature, and is different for each state of matter. Liquid water has one of the highest specific heats among common substances, about 4182 J/K/kg at 20 °C; but that of ice just below 0 °C is only 2093 J/K/kg. The specific heats of iron, granite, oak wood, and hydrogen gas are about 449, 790, 2400, and 14300 J/K/kg, respectively. While the substance is undergoing a phase transition, such as melting or boiling, its specific heat is technically infinite, because the heat goes into changing its state rather than raising its temperature.

The specific heat of a substance, especially a gas, may be significantly higher when it is allowed to expand as it is heated (specific heat at constant pressure) than when is heated in a closed vessel that prevents expansion (specific heat at constant volume). These two values are usually denoted by {\displaystyle c_{P}} c_{P} and {\displaystyle c_{V}} c_{V}, respectively; their quotient {\displaystyle \gamma =c_{P}/c_{V}} {\displaystyle \gamma =c_{P}/c_{V}}is the heat capacity ratio.

In some contexts, however, the term specific heat capacity (or specific heat) may refer to the ratio between the specific heats of a substance at a given temperature and of a reference substance at a reference temperature, such as water at 15 °C;[4] much in the fashion of specific gravity.

Specific heat relates to other intensive measures of heat capacity with other denominators. If the amount of substance is measured as a number of moles, one gets the molar heat capacity instead (whose SI unit is joule per kelvin per mole, J/K/mol). If the amount is taken to be the volume of the sample (as is sometimes done in engineering), one gets the volumetric heat capacity (whose SI unit is joule per kelvin per cubic meter, J/K/m3).

One of the first scientists to use the concept was Joseph Black, 18th-century medical doctor and professor of Medicine at Glasgow University. He measured the specific heat of many substances, using the term capacity for heat.

Answered by mahjabeen934

The dimensional formula of Specific Heat Capacity is given by,

M0 L2 T-2 K-1

Where,

M = Mass

K = Temperature

L = Length

T = Time

Derivation

Specific Heat Capacity (C) = Heat × [Mass × Temperature]-1. . . . (1)

The dimensional formula of mass and temperature = [M1 L0 T0] and [M0 L0 T0 K1] . . . .(2)

Since, the dimensions of Heat Energy = Dimensions of Work Done

And, Work = Force × displacement

= M × a × displacement = [M] × [M1 L1 T-2] × [L]

∴ the dimensional formula of Heat energy = M1 L2 T-2 . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Specific Heat Capacity = Heat × [Mass × Temperature]-1

Or, C = [M1 L2 T-2] × [M1 L0 T0]-1 × [M0 L0 T0 K1]-1 = [M0 L2 T-2 K-1].

Therefore, specific heat capacity is dimensionally represented as [M0 L2 T-2 K-1].

⇒ Check Other Dimensional Formulas:

Dimensions of Pressure Gradient

Dimensions of Current Density

Dimensions of Impedance

Dimensions of Linear Density

Dimensions of Rotational Kinetic Energy

JEE Related LinksIIT JEE MainsJEE Main Online Paper 2017Books for JEE AdvancedPhysics for JEE AdvancedHoffmann Bromamide Degradation ReactionJEE Main 2019 Exam PatternEnergy Stored in a CapacitorJEE Advanced Eligibility CriteriaJEE Advanced Marking SchemeMathematics Syllabus

Join BYJU'S JEE Learning Program

Submit

Derive the dimension of specific heat. ​

Answers

Derive the dimension of specific heat.