A certain metal container has the following dimensions: 30 cm x 15 cm x 2.3 cm.

Question

A certain metal container has the following dimensions: 30 cm x 15 cm x 2.3 cm. 1.0 mol of N2 gas at 27 oC is inside the container. The container can withstand 250,000 lbs of force. Cs = 1.1 J g · oC for nitrogen gas.

1. If 30.8 kJ of heat is added to the nitrogen gas raising its temperature, what is the resulting force exerted by the gas?

2. Will the container remain intact?

Hints: The surface area of the container can be determined by adding up the area of each ot the six faces. Use the ideal gas law to get pressures. Use the specific heat to determine the final temperature of the nitrogen gas. Use P = F A to get force.

Explanation / Answer

surface area = 2 (30*15+ 15*2.3 + 30*2.3 ) cm2 =1107 cm2 =1107*0.0001 m2 =0.1107 m2

Volume = 30*15*2.3 =1035 cm3=1035*0.001=1.035 L

R= 0.08206 L.atm/mole.K, T =27+273.15= 300.15

from PV= nRT Pressure = nRT/V= 1*0.08206*300.15/ 1.035 =23.79 atm

From F= PA F= 23.79*101325 N/M2* 0.1107 M2 =266844.8 N

b) from delU= Mass* specific heat * temperature difference= 28 ( 1 mole of nitrogen)* 1.1 * (t-27)

38*1000= 28*1.1* (t-27)

t-27= 38*1000/(28*1.1)=1233.7

t= 1273.7+27= 1260.7 deg.c

The temperatur is significant to keep the container intact

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