Question

A piston containing a gas is compressed from a volume of 8.70 L to 1.25 L against a constant pressure of 2.75 atm. while there is a heat loss by the system of 210 J. Calculate ΔE in kJ for the overall process.

Answer 1

The change in internal energy (ΔE) of a gas that is compressed from 8.70 L to 1.25 L at 2.75 atm with a heat loss of 210 J is 1.864 kJ.

Step-by-step explanation:

To calculate the change in internal energy (ΔE) for a gas that is compressed from a volume of 8.70 L to 1.25 L against a constant pressure of 2.75 atm while experiencing a heat loss of 210 J, we use the first law of thermodynamics. This law is stated as ΔE = q + w, where ΔE is the change in internal energy, q is the heat added to the system, and w is the work done on the system.

Given that the process involves a heat loss, we consider q to be negative, so q = -210 J. Next, we calculate the work done on the system by compression, using w = -PΔV, where P is the constant pressure and ΔV is the change in volume. It's important to remember that work done on the system is negative, as the system is being compressed.

To find ΔV, we subtract the final volume from the initial volume: ΔV = 1.25 L - 8.70 L = -7.45 L. However, to use this value in the equation, we need to convert it to the units of atm·L, the standard unit of energy in this context. Also, 1 L·atm is equivalent to 101.3 J. Therefore:

w = -2.75 atm × (-7.45 L) = 20.4875 atm·L × 101.3 J/atm·L = 2074.39875 J (rounded to 2074 J).

Now, by substituting the values for q and w into the first law of thermodynamics, we get: ΔE = q + w = -210 J + 2074 J = 1864 J.

To express ΔE in kilojoules (kJ), we convert joules to kJ by dividing by 1000: ΔE = 1864 J / 1000 = 1.864 kJ.

Answer 2

To calculate the change in internal energy of the gas, use the equation ΔE = Q - P(Vf - Vi), where Q is the heat transferred, P is the external pressure, Vf is the final volume, and Vi is the initial volume.

Step-by-step explanation:

In this problem, we are given the initial volume (Vi), final volume (Vf), constant external pressure (P), and the heat transferred (Q). We need to find the change in the internal energy (ΔE) of the gas. The change in internal energy can be calculated using the equation:

ΔE = Q - P(Vf - Vi)

Plugging in the given values:

1. Initial volume, Vi = 0.200 L
2. Final volume, Vf = 3.50 L
3. External pressure, P = 0.995 atm
4. Heat transferred, Q = 117 J

Substituting the values into the equation:

ΔE = 117 J - (0.995 atm)(3.50 L - 0.200 L)

Solving the equation will give us the change in internal energy, ΔE, in joules.