Using the definitions of enthalpy, heat capacity at constant volume and heat cap

Question

Using the definitions of enthalpy, heat capacity at constant volume and heat capacity at constant pressure show that for 1 mole of ideal gas the following relation holds: (b) quation Q5.a (4 marks) In a 200 cm3 container, a certain amount of 02 gas is held with a piston at equilibrium with the external pressure being 1 bar. The temperature of the gas is 298 K. When 2 J of heat is supplied, the gas expands against the constant external pressure. Assuming that no heat is lost from the gas, calculate: (c) (i) the new volume it occupies after the expansion (ii) the work done in the expansion (i) the change in internal energy of the gas (iv) the change in enthalpy of the gas. (4 marks) (2 marks) (2 marks) (3 marks)

Explanation / Answer

Part b

Heat capacity at constant volume

Cv = dU/dT

Heat capacity at constant pressure

Cp = dH/dT

For 1 mol of an ideal gas equation

PV = RT

d(PV) = d(RT) = RdT

R is gas constant

From the definition of Enthalpy

For 1 mol of ideal gas

dH = dU + d(PV)

CpdT = CvdT + RdT

Cp = Cv + R

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