Write the dimension formula of molar specific heat. Let the dimension formula of mole be [μ].
The dimensional formula for molar specific heat is,
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What is the equation of state for isothermal process? Plot P versus V graph and P versus T graph for isothermal process for an ideal gas. Discuss the isothermal process using first law of thermodynamics.
An ideal gas equation is, PV = nRT Since in isothermal process, T is constant, therefore the equation of state for isothermal process reduces to PV = constant P versus V graph and P versus T graph for isothermal process is as shown below. According to first law of thermodynamics,
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Derive the expression for the work done by the gas during isothermal expansion.
We know work done by or on the system is given by
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Derive an expression for the work done by a gas undergoing expansion from volume V1 to V2.
Let us consider an ideal gas enclosed in a cylinder fitted with massless and frictionless piston. Let A be the area of cross-section of piston. Let V be the volume and P be the pressure exerted by gas on the piston. The piston is kept in equilibrium by applying pressure P from outside.
Let the applied pressure be decreased by infinitesimally small amount, so that the piston moves by infinitesimal distance dx. The amount of work done by the gas in infinitesimal expansion is, where dV = Adx, the infinitesimal increase in volume. Total work done by gas in expanding it from volume V1 to V2 can be obtained by integrating equation (1) from V1 to V2 i.e.
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Derive an expression for the work done in adiabatic process.
Consider a unit mole of gas contained in a perfectly non-conducting cylinder provided with a non-conducting and frictionless piston.
Let Cv be the specific heat of gas at constant volume.
Let at any instant, when the pressure of gas is P, the gas be compressed by small volume dV.
Then work done on the gas is,
dW = PdV
Total work done on gas to compress from volume V1 to V2 is given by
...(1)
According to first law of thermodynamics,
For adiabatic process,
∴ PdV = -dU =
∴
where,
T1 is the temperature of gas when volume is V1 and T2 when volume is V2.
Thus, work done is given by,
Therefore,
The above expression gives us the amount of work done in adiabatic process.
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Derive the equation of state for adiabatic process. Plot P versus V graph for the process.
According to the first law of thermodynamics, In adiabatic process, no heat is allowed to exchange between the system and surrounding, therefore dQ = 0. Thus,
...(1) 
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