A piston-cylinder assembly in an air atmosphere of p = 1 atm (= 1.013 bar) conta

Question

A piston-cylinder assembly in an air atmosphere of p = 1 atm (= 1.013 bar) contains 1 kg of nitrogen. The initial volume of the nitrogen is 1 m^3, and its initial pressure is 1 atm. The side of the cylinder is heated such that the heat transfer to the nitrogen causes its volume to double. Ignoring friction and assuming a specific heat ratio which is constant at 1.4.

What is the heat transfer for the process, in kJ? The nitrogen may be modeled as an ideal gas. You may assume that the nitrogen is in equilibrium at state 2.

Explanation / Answer

P*V = n * R* T

now Q - W = delta U

so n*Cp *(T2-T1) - P*(V2-V1) = n* Cv*(T2-T1)

so n* Cp* (T2-T1) - n*(Cp/1.4) (T2-T1) = 101300* (2-1)

so n* Cp* (T2-T1) (1- 1/1.4) = 101300

so Q= 101300/ (1-(1/1.4)) = 354550 J= 354.55 KJ

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