Homework 2, due Thursday 1/24 at the beginning of class List any assumptions you

Question

Homework 2, due Thursday 1/24 at the beginning of class List any assumptions you need to make to solve the assigned problems Consider a cylinder filled with air with a piston and spring arrangement on top. as shown in the figure below. The external pressure is 1 bar. the initial temperature of the air in the cylinder is 25 degree . The no-load length of the spring is 50 cm and the spring constant is 40.000 N/m. The piston weighs 500 kg. You can assume the constant volume heat capacity of air to be constant at 20.9 J/(mol K). Compute the initial pressure of the gas in the cylinder Compute how much heat must be added to the gas in the cylinder for the spring to compress by 2 cm. You can treat the air as an ideal gas and assume that Delta n is given by the product of the constant volume heat capacity and Delta T.

Explanation / Answer

initial pressure = ATM + weight of piston air inside cylinder is supporting / area.

since length increased in piston is 5cm.

we have Force = kx = 40,000 * 0.05 = 2000 N => 200 kg is supported by spring.

=> 300 kg is supported by air pressure inside cylinder.

300 kg = 3000N / r2 = 42441.318 Pascals = 0.42441 Bar.

=> pressure inside cylinder is = 1+0.42441 bar = 1.42441 Bar.

2)

AS no. of moles are not changing

P1*V1/T1= P2 * V2 /T2

P1 = 1.42441Bar.

V1 = A * .15,

T1 = 273+25 = 298 K

now the spring to compress 2 cm means lenght of spring becomes 53cm.

i.e. pressure P2 =1Bar + ( 5000 - 40000 * 0.03 )/ r2 = 1.538 Bar.

V2 = A * 0.17 ;

using equation we have T2 = 364.7 K = 91.7 degree celcius.

there fore heat added = 20.9 * change in temp. = 20.9 * 66.7 = 1394.03 J /mol

number of moles = PV/T*R

n = 5.07 moles

heat added = 1394.03 * n

u = 7065.04J

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