Six g of air is contained in the cylinder shown in Fig. The air is heated until the piston raises 50 mm. The spring just touches the piston initially. Calculate
Text Solution
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Sol. The pressure in the air when the piston just raises from the stops is found by balancing the forces on the piston:
PA = P atm A + W 
= (100000) 
+ (300) (9.81)
∴ P = 193700 Pa or 193.7 kPa
The temperature is found from the ideal-gas law:
T = 
= 
= 530 K
The work done by the air is considered to be composed of two parts: the raise the piston and the work to compress the spring. The work required to raise the piston a distance of 0.05 m is
W = (F) = (P) = (193.7) 
(0.05) = 0.304 kJ
The work required to compress the spring is W = ½ Kx 2 = 0.5 kJ. The total work required by the air to raise the piston is
W = 0.304 + 0.5 = 0.804 kJ.
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