In the cylinder under the piston there is air under pressure p1 = 2.0 * 10 to the fifth power of Pa

| February 7, 2021 | education

In the cylinder under the piston there is air under pressure p1 = 2.0 * 10 to the fifth power of Pa and at a temperature of T1 = 300 K. What mass m must be put on the piston after heating the air to a temperature of T2 = 330 K in order to return the piston to its original position?

To determine the required weight of the load to return the specified piston to its original position, we use the equality: P1 * T2 / T1 = P2 (steady-state pressure) = P1 + Pgr = P1 + Pgr = mgr * g / S, from where we express: mgr = (P1 * T2 / T1 – P1) * S / g.

Constants and variables: P1 – initial pressure (P1 = 2 * 10 ^ 5 Pa); T2 – final air temperature (T2 = 330 K); T1 – initial air temperature (T1 = 300 K); S is the area of ​​the specified piston (S = 30 cm2 = 3 * 10 ^ -3 m2); g – acceleration due to gravity (g ≈ 10 m / s2).

Calculation: mgr = (2 * 10 ^ 5 * 330/300 – 2 * 10 ^ 5) * 3 * 10 ^ -3 / 10 = 6 kg.

Answer: It is required to put a weight of 6 kg on the indicated piston.



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