Analyze the Change in Internal Energy of the Gas in a Cylinder

How to calculate the change in internal energy of the gas in a cylinder?

Calculating the Change in Internal Energy of the Gas

The change in internal energy of the gas is -1689.06x10 J.

To calculate the change in internal energy of the gas, we need to consider the heat added to the gas and the work done by the gas during the process.

Calculating Heat Added to the Gas

First, we calculate the heat added to the gas using the power and time:

Q = P × t

Given that the power of the electric heater is 80W and it operates for 7.5 minutes:

Q = 80W × 7.5 minutes = 600J

Calculating Work Done by the Gas

Next, we calculate the work done by the gas using the equation:

W = P(V2 - V1)

Given that the gas expands from 5 to 11 L at a constant atmospheric pressure of 281.61x10 Pa:

W = 281.61x10 Pa × (11L - 5L) = 1689.66x10 J

Calculating Change in Internal Energy

Finally, we can calculate the change in internal energy of the gas using the equation:

ΔU = Q - W

ΔU = 600J - 1689.66x10 J = -1689.06x10 J

Therefore, the change in internal energy of the gas in the cylinder is -1689.06x10 J.

Answer:

The change in internal energy of the gas is -1689.06x10 J.