Two massless, frictionless pistons are inside a horizontal tube opened at both e

Question

Two massless, frictionless pistons are inside a horizontal tube opened at both ends. A 10-cm-long thread connects the pistons. The cross-sectional area of the tube is 20 cm2. The pressure and temperature of gas between the pistons and the outside air are the same and are equal to P = 1.0×10^5N/m2 and T = 25 C. At what temperature will the thread break if it breaks when the tension reaches 26N?
N Two massless, frictionless pistons are inside a horizontal tube opened at both ends. A 10-cm-long thread connects the pistons. The cross-sectional area of the tube is 20 cm2. The pressure and temperature of gas between the pistons and the outside air are the same and are equal to P = 1.0×10^5N/m2 and T = 25 C. At what temperature will the thread break if it breaks when the tension reaches 26N?
N Two massless, frictionless pistons are inside a horizontal tube opened at both ends. A 10-cm-long thread connects the pistons. The cross-sectional area of the tube is 20 cm2. The pressure and temperature of gas between the pistons and the outside air are the same and are equal to P = 1.0×10^5N/m2 and T = 25 C. At what temperature will the thread break if it breaks when the tension reaches 26N?

Explanation / Answer

Here Volume of the container is constant.

Excess pressure needed to break the thread, P = F/A

= 26/(20*10^-4)

= 1.3*10^4 N/m^2

P1 = 1*10^5 N/m^2

T1 = 25 + 273 = 298 K

P2 = 1*10^5 + 0.13*10^5 = 1.13*10^5 N/m^2

T2 = ?

Apply, At constant volume

P1/T1 = P2/T2

T2 = (P2/P1)*T1

= (1.13/1)*298

= 387.4 K

= 387.4 - 273

= 114.4 degrees celsius

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