Question

A chemical reaction transfers 8250 J of thermal energy into 11.8 moles of an ideal gas while the system expands by 2.00 x 10⁻² m³ at a constant pressure of 1.65 x 10⁵ Pa. Find the change in the internal energy (in J).

Answer 1

The change in internal energy of the ideal gas is calculated using the first law of thermodynamics. Given the heat transfer of 8250 J and the work done by the gas at 3300 J, the change in internal energy (ΔU) is 4950 J.

Step-by-step explanation:

To calculate the change in internal energy (ΔU) of an ideal gas, you can use the first law of thermodynamics, which states that ΔU = Q - W, where Q is the heat transferred to the system, and W is the work done by the system.

In the case provided, the heat transferred (Q) is 8250 J and the work done by the system (work is positive when the system does work on the surroundings) can be found by the formula W = PΔV, where P is the constant pressure and ΔV is the change in volume.

Here, P is 1.65 x 10⁵ Pa and ΔV is 2.00 x 10⁻² m³.

The work done W by the gas is then W = PΔV

= (1.65 x 10⁵ Pa)(2.00 x 10⁻² m³)

= 3300 J.

Now that you have the values for Q and W, you can find the change in internal energy: ΔU = Q - W

= 8250 J - 3300 J

= 4950 J.

Hence, the change in the internal energy of the gas is 4950 J.