Question

A cylinder-piston system contains an ideal gas at a pressure of 1.5 * 10^5 Pa. The piston is pushed out, allowing the gas to expand from an initial volume of 0.002 m^3 to a final volume of 0.006 m^3. The system absorbed 32 J of heat during the process. What is the change of internal energy?

a) 16 J
b) 32 J
c) 48 J
d) 64 J

Answer 1

The change of internal energy in the cylinder-piston system is not among the provided options, as the calculation gives a value of -568 J, which is not listed.

Step-by-step explanation:

In order to find the change of internal energy for an ideal gas in a cylinder-piston system, we need to apply the first law of thermodynamics, which is ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.

In this scenario, the system absorbs 32 J of heat (Q = 32 J). The work done by the system during expansion (W) can be calculated using the formula W = PΔV, where P is the pressure and ΔV is the change in volume. Here, P = 1.5 x 105 Pa and ΔV = 0.006 m3 - 0.002 m3 = 0.004 m3. So, W = (1.5 x 105 Pa)(0.004 m3) = 600 J.

Since the work is done by the gas on the surroundings, it is positive, and the heat added to the system is also positive; we plug the values into the first law of thermodynamics to get:

ΔU = Q - W = 32 J - 600 J = -568 J.