Question

A cube 17 cm on each side contains 2.2 g of helium at 20∘C. 1100 J of heat energy are transferred to this gas.

Part A

What is the final pressure if the process is at constant volume?

Express your answer to two significant figures and include the appropriate units.

Part B

What is the final volume if the process is at constant pressure?

Express your answer to two significant figures and include the appropriate units.

Answer 1

Given Data

Initial volume,v1 = 17 cm = (17 x 10^-2)^3 =4.913 x 10^-3 m^3

No. of moles, n1 = 2.2/4 = 0.55

Temperature, T1 = 20 deg = 20+273 = 293K

From ideal gas equation, PV = nRT

=>P1*(4.913 x 10^-3) = 0.55 *(8.314)*293

=>P1 = 266.67 KPa

Energy provided = 1100J

A] Constant volume => Final pressure be P2 and temperature be T2

1100 = nc_vΔT

1100 = 0.55*12.5*(T2-293)

=>T2-293 = 160.26

=>T2 = 453.26 K

Now P1/T1 = P2/T2

=> 266.67*10^3 /293 = P2/453.26

=>P2 = 412525 Pa = 4.125*10^5 Pa

B]Constant pressure => Final volume be V3 and temperature be T3

1100 = mc_pΔT = 2.2*5.19*(T2-293)

=>T3-293 = 96.34

=>T3 = 389.34 K

Now V1/T1 = V3/T3

=> (4.913 x 10^-3)/293 = V3/389.34

=>V3 = 6.528 x 10^-3 cm^3 = 0.653 m^3

(or)

Now V1/T1 = V3/T3

=> (4.913 x 10^-3)/293 = V3/453.26

=>V3 = 7.6 x 10^-3 cm^3 = 0.76 m^3