# An Amount Q of Heat is Added to a Monatomic Ideal Gas in a Process in Which the Gas Performs a Work Q/2 on Its Surrounding. - Physics

An amount Q of heat is added to a monatomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding. Find the molar heat capacity for the process

#### Solution

Given:
Amount of heat given to the gas = Q
So, ∆Q = Q

Work done by the gas, Δ W = Q/2

From the first law of thermodynamics,

ΔQ = ΔW +Δ U

=> triangle "U" = "Q" - "Q"/2 = "Q"/2

For a monoatomic gas,

triangle "U"= 3/2 "n""R""d""T"

=> "Q"/2 = "n""d""T" xx3/2 "R"

⇒ Q = 3nRdT

Again, for expansion at constant pressure,
Q = nCpdT,
where Cp is the molar heat capacity at constant pressure.
So, 3RndT = nCpdT
⇒ Cp = 3R

Concept: Kinetic Theory of Gases and Radiation - Introduction of Kinetic Theory of an Ideal Gas
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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 5 Specific Heat Capacities of Gases
Q 8 | Page 78