Question

If a gas absorbs $200J$ of heat and expands by $500$ cm${}^3$ against a constant pressure of $2\times {10}^{5}N{m}^{-2},$ then the change in internal energy is:

Answer 1

Correct Answer: 100

To determine the change in internal energy (ΔU) of the gas, we apply the first law of thermodynamics, which states ΔU = Q - W, where Q is the heat absorbed by the system, and W is the work done by the system. Given:

• Q = 200 J (heat absorbed)
• The gas expands by 500 cm³. Converting this to cubic meters, 500 cm³ = 500 × 10^-6 m³.
• Constant pressure P = 2 × 10⁵ N/m²

The work done by the gas during expansion against constant pressure is W = PΔV, where ΔV is the change in volume. Calculating W:
W = 2 × 10⁵ N/m² × 500 × 10^-6 m³ = 100 J.
Substituting the values into the first law of thermodynamics gives:
ΔU = Q - W = 200 J - 100 J = 100 J.
The change in internal energy is 100 J, which falls within the given range of 100, 100.