Heating gas in a rigid container

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Problem: Heating gas in a rigid container
A fixed amount of ideal gas in a rigid container warms from 300 K to 450 K. Its initial pressure is 100 kPa.
Question: Find its final pressure.
Givens:
- T₁ = 300 K
- T₂ = 450 K
- p₁ = 100 kPa
- V fixed
Assumptions: Fixed amount of ideal gas in a rigid sealed vessel; equilibrium states; temperatures are absolute.
Choices (LaTeX):
A. 150\ \mathrm{kPa}
B. 100\ \mathrm{kPa}
C. 66.7\ \mathrm{kPa}
D. 250\ \mathrm{kPa}

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.