Question

A cylinder-piston system contains an ideal gas at a pressure of 1.0 x 10^5 Pa. The piston is pushed in, compressing the gas from an initial volume of 0.0005 m^3 to a final volume of 0.0003 m^3. The system absorbs 25 J of heat during this process. What is the change in internal energy?

a) -50 J
b) -25 J
c) 25 J
d) 50 J

Answer 1

The change in internal energy of the gas is 5 J, resulting in a final value of 25 J.

Step-by-step explanation:

The change in internal energy (ΔU) of an ideal gas is equal to the heat transfer (Q) minus the work done (W) by the gas. In this case, the system absorbs 25 J of heat, so ΔU = Q - W. Since the work done is given by the equation W = -PΔV, where P is the pressure and ΔV is the change in volume, we can find the work done by calculating the product of the pressure and the change in volume. The pressure is given as 1.0 x 10^5 Pa, and the change in volume is (0.0003 m^3 - 0.0005 m^3) = -0.0002 m^3. Therefore, W = -(1.0 x 10^5 Pa)(-0.0002 m^3) = 20 J. Substituting this value into the equation, we have ΔU = 25 J - 20 J = 5 J. Therefore, the change in internal energy is 5 J, which means the correct answer is (c) 25 J.